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EPR....Exhale Pressure Relief
where when you start to exhale the machine reduces the pressure by whatever setting you have chosen so that it's not so difficult to exhale. Some people like it, need it and wouldn't do without it and some people simply don't need it.
I used 10 cm pressure for a period of time without any exhale relief at all and then I got a machine with a little more advanced exhale relief and I found I really liked it. Do I absolutely "need" it...no but I found it made my breathing on the cpap machine a lot more natural feeling and easy so I continued to use it simply because I liked it.

Different brands of machines have different forms of exhale relief. For some one method might feel better than another way of offering that relief.

So with the ResMed machines EPR has 3 levels of pressure reduction 1, 2 and 3 with a setting of 1 there is a 1 cm reduction in pressure, a setting of 2 is 2 cm reduction and with a setting of 3 there is a 3 cm reduction.
Example: Suppose your prescribed pressure is 10 cm so the machine is set to 10 cm and you aren't comfortable exhaling against 10 cm so the EPR feature is turned on...at a setting of 1 the pressure during exhale is reduce from 10 to 9 and with a setting of 2 it's reduced from 10 to 8 and at at setting of 3 the pressure will reduce to 7 from 10 upon exhale.

The difference between inhale and exhale is called pressure support. Don't ask me why they call it that ...they just do.

ResMed cpap/apap machines have a maximum Pressure Support (PS) or that 3 cm reduction that EPR offers.

Bilevel machines offer greater than 3cm Pressure support. It is the difference between inhale and exhale that offers this "comfort" feature. For a lot of people that 3 cm pressure support is more than enough to be comfortable with and remember some people use less or none.
Some people find they need more than 3 cm for any number of reasons and that's when bilevel devices (BiPap is a Respironics marketing term for bilevel and VPAP is ResMed's marketing term) are sometimes needed. We have no way to know if you need a bilevel device at this time.

The reason I suggested the ResMed with EPR form of exhale relief is that it feels just like a bilevel machine would feel at 3 cm Pressure Support setting because that's how it works.

Respironics machines go about their exhale relief differently and the most you can get in terms of reduction is 2 cm and it's flow based so if you don't breathe forcefully you might not even get the full 2 cm. It isn't as dramatic of a reduction as the way EPR works. It's not crap though...I used Respironics AFlex relief for years and it's actually quite nice...but then I tend to adjust easily to just about anything.

There's no way for us to know which brand might suit you the best and since we don't even know what your pressure needs are going to be I suggested the ResMed because I know how it works and if you happen to need pressures in the teens I think (based on my past experience on how EPR feels and compared it to how a bilevel machine feels) that the ResMed's way of doing EPR would sort of cover all potential bases as best we can in this situation.

Qualifying for bilevel devices (for insurance to cover the cost) is a lot harder and there's going to be special requirements that need to be met. We don't know if you would meet those requirements or not.
This is where the titration sleep study comes in...you find out exactly what pressure you need and you have a starting point as to which machine you need.

CPAP/APAP machines offer single pressures up to 20 cm.
Bilevel devices offer dual pressures (that's when you have a separate pressure for inhale and separate for exhale) that go up to 25.

CPAP/APAP machines aren't technically bilevel devices but using the exhale relief available they can function to some extent like a true bilevel device and ResMed's exhale relief is more like true bilevel except you can only go to 3 cm difference whereas with a true bilevel you can have 4 or 5 cm (or more) difference between inhale and exhale.
It's the difference that offers the exhale relief.
Remember some people don't need any relief and some people do and some people just like it.
The difference between a 3 cm drop and a 4 cm drop isn't huge in how it feels and I think most people would/could do well with 2 or 3 cm drop.
Hence the recommendation for the ResMed...covering potential bases as best we can without knowing more about exactly what pressures you are going to need.

You have already gotten terrific advice. I will just add some comments on machine purchase.

Basically, you have two choices - insurance or buy your own.

You now know from your sleep study that you need and qualify for a machine. The next step is to check with your insurance company and find out how much they will pay and the must important part, how much YOU have to pay. Not what percentage you will have to pay, but the actual dollar amount. It's a screwy system where the insurance company pays the Durable Medical Equipment company (DME) a fixed price whether the latter gives you the cheapest, dumbest machine on the market or a top of the line machine with all the bells and whistles. The insurance company doesn't care which you get. The DME has incentive to maximize his profit by giving you a low-end, dumb machine. The cpap manufacturers make it easier for them by creating lines of machines that are very similar in name and appearance - often a single word is the difference between the low-end and the high-end machine.

Every insurance company is different. There have been examples where people's copay has been nearly equal to what they could have bought the machine for from cpap.com. And the insurance company paid-for machine may come as a sort of lease-to-own arrangement and will probably also require you to provide compliance data for them to continue paying for it. My point is that you have to talk to your particular insurance company and find out how they handle cpap machines. Part of the problem is that the insurance and the DME price are based on a "list price" system that no knowledgeable cpap user would pay. It is a crazy system and it can end up costing you money if you are not careful. When you talk to the insurance company, take careful notes. Ask them if the information they are giving you is available on their website and where you can find it. If something is confusing or uses terms that you don't understand, ask questions.

My suggestion would be to come back here and ask for advice before accepting any machine.

For purchase without insurance, there are two paths - new or used.

For non-insurance new purchases, our sponsor's site cpap.com has about the best prices you'll find for brand new machines sold with a warranty. This will give you a benchmark to see if getting a machine through insurance is a good deal or not.

For used machine - the cheapest option of all, the generally recommended options are secondwindcpap.com or craiglist. Secondwind buys used machines from people, reconditions them and resells them WITH a warranty. People have had very good experience with them and they have a good reputation.

Sometimes, forum members right here have used machines that they sell at reasonable prices - that is also an option. Although you do have to find out if you are dealing with a regular or some unknown person who just pops in and tries to unload a low-end machine that he knows nothing about for "list price". Those get shot down pretty quickly here to the dismay of their posters. People here will let you know who the people are that are safe to deal with.

The final and cheapest option is also the most risky, time consuming and difficult - craigslist. 90% of the machines people list for sale are overpriced because the people selling them base their price on the fantasy list price. The other 10% can be good deals but you have to worry about things that don't when you buy from other places - like was the machine previous used by a smoker and now smells of smoke. Once it gets into the machine it usually can't be completely removed without replacing some of the internal parts - you can search the forum and find thread where people have dealt with this. Sometimes, you can get lucky - I got the machine in my profile for only $100 with only 95 hours on it because the guy got a new machine from his insurance company and didn't need/want it any more. But that was definitely the exception, not the rule. You will also be competing with people from this forum who buy used machines to resell them - I won't mention any names, but you know who you are! If it's someone local to you, you have an edge in that you can pick it up from the seller and he doesn't have to bother to ship it and worry about a check bouncing or paypal chargeback but gets cash in his hand. Someone in another state was trying to buy the machine that I scooped up.