The things you need to ask about are breakdown of your apnea events during the home sleep study. They will classed into obstructive apnea events, central apnea events, and hypopnea events. If they are virtually all obstructive apnea and hypopnea events then you are a likely candidate for a CPAP.
Ask to see the results from you in lab test which is a titration study to determine what pressure works for you. They increase the pressure over the night to determine how much pressure is needed to control the obstructive events. Generally as the pressure goes up the obstructive events stop at some point as the pressure holds the airway open. However, more pressure can generate more central apnea events. Central apnea is when you do not breathe but the air flow is not blocked. They are sometimes called clear airway events. So, the trick is to determine how much pressure will stop the obstructive apnea without causing central apnea.
As far as a machine goes, there are automatic ones (APAP) and manual ones (CPAP). The APAP machines cost very little more than a manual fixed pressure CPAP machine. I would resist being given a fixed pressure CPAP machine. Insist on an APAP. If necessary they can be set to CPAP mode. There is no disadvantage of an APAP other than a small (<$100) extra cost.
A BiPAP mainly provides more pressure than an APAP. APAP machines max out at 20 cm of water pressure. A BiPAP will go up to 25 cm of pressure. They also can increase the pressure between inhale and exhale more. The unfortunate part is that going over 20 cm pressure can be quite uncomfortable for sleeping. My thoughts are not to go there unless you have to. That is why you should ask about the pressure needed during the titration study, and if a BiPAP machine is really necessary.
I am less sure about the market in the US, as I am in Canada. Here there can be a huge difference in the cost of a machine from an on line vendor than from a sleep clinic. My sleep clinic wanted me to pay $2400 for a machine. I asked for a prescription and bought one on line for about $900. But, I was paying out of my own pocket. You may not get that freedom to buy on line if your insurance company puts restrictions on what you can do. It sounds like you have a generous insurance plan, and it may be all covered if you just go with the flow. Just make sure you get the right machine for your needs, and have the ability to exchange it if it does not work for you.
In Canada the next typical step from where you are is to get a trial machine and then use it at home for 2-3 weeks to see if it works and you can tolerate the use of it. Then, at least here, you get the option of buying it or not. I took the "or not" and just bought a better one on line for much less cost. As for brands I think ResMed is best, Phillips DreamStation is second best. I would avoid the other brands.
Hope that helps some,