First of all, get used to the FACT that nothing about scuba is inexpensive. Not computers, not regulators, not BCs, nothing! It is all expensive. If you're worried about the price of a computer as a first purchase, you're about to embark on the wrong hobby/sport. Set aside about $2500 to get started with decent gear.
A Nitrox compatible dive computer lets you select the % of O2 you have in your tank. By default, the computer will assume 21% or AIR. Later on you may want to get extended bottom time or decreased surface interval (waiting around) time and you may take a Nitrox class. With Nitrox you get a lot of benefits but the cost is increased complexity. The Nitrox compatible computer can handle it for you. IF you remember to set it for the blend you are actually diving...
I have a Dive Rite Nitek DUO computer and I like it a lot. However, the downloader is crap and the software isn't much to write home about. But, as a computer, it is terrific. Look around, ScubaToys usually sells the computer with the downloader for less than others sell the computer alone.
Buying a computer should be one of the LAST things you buy, not one of the first. I got by for 20 years without a computer and only bought one to deal with Nitrox. Dive tables will get you by for a very long time and they are about the only thing in diving that is cheap.
Your OW training classes are so guided and the dives are so short you won't have any need for a computer. What you will need is your personal gear: mask, snorkel, fins and gloves. Most shops require you have these when you take the course. You can buy them wherever you want but conventional wisdom would have you buy them from the shop that is training you. What you probably DON'T want to do is show up with brand new stuff you bought from LeisurePro. Figure about $200-$300 for this stuff. Maybe a little more, maybe a little less but you should be buying stuff that is high quality and will last for a few years.
Richard