First some clarification:
When you record from LP at 192/24 or whatever sample rate, you are creating a WAV file (which is uncompressed) and that is why it takes up so much hard drive space. After the wav is saved, the program then transcodes to the lossy compression format of your choice (MP3, WMA, etc).
I'm not familiar with that particular program, but if it will transcode directly to a compressed format, then there is no reason to save the wav file when it is done and disk space should not be a problem. There may be settings that allow you to specify whether you want to keep the wav or delete it as soon as it is done transcoding. If you are recording the entire LP side before transcoding, then you will need quite a bit of free space even if it is deleted afterwards.
Here's the catch. There are only a few sound cards that actually record at 192/24. If you have any flavor of SoundBlaster it DOES NOT - despite what the marketing literature says. The EMU chip they use handles everything internally at 48/16 so even if your program is set to 192/24, the hardware will resample on the fly to 48/16 while capturing the sound and then convert it back to 192/24 (by simply zero extending the 16 bits to 24 and duplicating the samples so you have 192K samples instead of 48K). There is no quality gain to be had by recording at 192/24 if you have such a card.
If you intend to burn an audio CD from the recording, then record at 48 kHz/16 bit and then resample to 44/16 in software. If you don't have an audio editor (or your recording program can't do it) then just record at 44/16. Even if your sound card can truly record at 192/24 you will have to resample to 44kHz and convert the bit depth to 16 to make a valid audio cd that will play in a cd/dvd player.
You can of course just burn a data CD with the MP3/WMA files on it but in order for it to play in your mother's cd/dvd player, the player must be able to decode MP3 on the fly - many newer ones can but you probably want a regular audio CD instead.
As for sound quality - the various encoding algorithms produce slightly different results and you would have to experiment with the different formats and bit rates to find what sounds best to you. For maximum compatibilty with other devices, use MP3 at 192 kbps or higher.