need to convert some records to MP3
I'm not sure how far you want to go with this, e.g. how much time, effort, & $ you want to spend... maybe you can take something from this that you can use?
To play the records 1st step of course is the turntable, where more mechanical aspects [tonearm, turntable drive mechanism etc.] matter. The cartridge matters too, but you may be able to save some money if this is a one-off by not worrying about how long the cartridge will last. I'm skeptical you'd find much quality in or with the usual USB turntable affairs for converting a record collection, or all in one units for that matter, & would suggest a regular turntable for home audio or perhaps one of the DJ models.
Optional but I think worth it if you had a home audio turntable, a small mixer can take the signal from the turntable, amplifying it as necessary, & provide the output signal to your PC/laptop. I think many DJ turntables might be designed to work with your PC/laptop already. Using the mixer you could make sure the signal was as high or loud as possible without overwhelming the PC/laptop audio electronics [e.g. clipping], allow you to adjust bass/treble &/or provide an equalizer, might have added filtering &/or FX, & would have a separate jack(s) for headphone monitoring of the signal going into your PC/laptop.
Alternatively you can always mic your stereo speakers -- using a mic to record what comes out of the speakers has been around a long time. You'd still have to have the turntable, but maybe you'd have use for the microphones when this project was over?
For the actual recording, if you wanted the least amount of noise your best bet might be an external recorder -- the electronics inside a PC add interference noise whether you're using the PC's on-board audio chipset, a sound card, or some USB audio. Otherwise look up the specs of how much noise whatever hardware will introduce & compare -- when it comes to digitizing the analog signal you probably won't find a whole lot of difference, so it's more about how much noise brand X will add vs. brand Y. You may well find that on-board chipset is as good as many add-ons, & probably better than some.
When you're recording line-in [the mono or stereo signal] the recording software itself isn't going to really effect the recording quality -- all it's doing is taking the ones & zeros your audio hardware gives it & writing that to a file. Higher end stuff lets you add FX on-the-fly, maybe lets you record more than 2 channels, may play back an existing track(s) while it records & so on. If your hardware supports higher bit depth & sampling rates you may need better software to use them, but that's more an oversight on the part of any developers who've left that out, & when the final goal is MP3s, probably irrelevant anyway.
You will probably want to record to .wav using your hardware's internal sampling rate [look it up but probably 48 rather than 44.1], then use a noise filter to try & get rid of most of the noise associated with vinyl records. Optionally you might want to do other processing, e.g. normalize, then convert that to MP3. If your MP3s are going to be 44.1 & you recorded at 48, look for software that can use dithering for that resample step. Audacity or Wavosaur should do what you need, but places like Musiciansfriend.com often have home versions of bigger name audio apps on sale -- if you can get the job done during the 30 trial check out Sony's Sound Forge.