I assume you mean compression as in MP3 compression and not dynamics compression. No, CD audio is about 10 megs per minute (
source), no matter what program you use to burn. You know how discs are labeled 80 minutes, 74 minutes, or similar? Your half-full disc probably has 35 - 40 minutes' worth of 16-bit, 44.1kHz stereo audio.
But no, there's nothing wrong with using Windows Media Player to burn your CD's. As I said before, your CD's will end up 88.2kb * 2 per second regardless of what you use to burn, and regardless of whether they started out as WAV, FLAC, MP3, OGG, MP4 or whatever. The source format can affect the end result insomuch as they have varying qualities and amounts of loss in their native formats. But you really aren't saving any extra quality by ripping CDs to 24/192, and no program can burn 24/192 to CD audio without downsampling.
It's important that you recognize the difference between burning an audio CD and burning a data CD containing audio files. You can burn excessively high bitrate audio files to a data CD as data files and get the satisfaction of seeing the entire disc used, but most CD players won't be able to play it. What it sounds like you have in mind is more a means of backup and archival than burning something useable in a hi-fi system.
If you are uncomfortable using WMP to master and burn, I like ImgBurn for burning discs. To master a layout, you have to do Tools --> Create CUE File. But beyond that, it's pretty simple and flexible, and it includes no malware. And it is much more flexible than WMP, allowing you to customize the pregap between tracks, and tweak CD text if you wish.
There are lots of other freeware and open source CD burner programs to be found on sites such as download.com and Snapfiles, but
pay attention to the components you're agreeing to install! I know Starburn Free, for example, includes piggyback scumware and you have to read very carefully to opt out. I don't recall whether CDBurnerXP includes adware / toolbars or not, but the advice in bold is worthwhile to keep in mind whenever installing anything regardless.
Roxio Easy CD Creator used to be my favorite commercial mastering / burning suite. It's probably the most intuitive CD burning software I've used, but it's very bloated.
Occasionally,
Giveaway Of The Day offers CD burning programs. If you check there from time to time, you might get lucky.