I have dabbled in this from time to time, and if I may would offer some suggestions:
1. Playing the original work. For vinyl, keep in mind that good (medium-high price) turntables offer a better sound than cheap ones, same for cartridges. Vinyl lovers will think nothing of paying e.g. $150 US upwards for just the cartridge, so an integrated turntable+cartridge on offer for say $100 is not likely to offer the best sound. For the record (pun intended) I use a mid-range Rega turntable ($400 or so) with a Rega cartridge ($150 or so), although previously I used a more expensive Garrott Bros ($400 30 years ago) until I felt like a new one was needed.
Historically, good component-level turntables do not output line level signal or digital/USB so you need an amplifier or preamplifier that will convert the cartridge level signal to line level. Someone will probably contradict me here, but I believe that the majority of newer turntables that offer e.g. a USB output will be optimized for convenience, not for sound quality.
Same for cassette playback systems, which originally varied from say $50 (cheap) to e.g. $500 plus (less cheap but also better). You need something that will get a good (or best) sound off the tape if possible, especially if this is a one time task; may involve selecting the correct tape type, bias, and dolby types according to how the original was recorded (especially if it is a live recording by an enthusiast, not just a commercial pre-recorded tape).
2. Recording into the computer (PC or Mac). You have to think about where the analog/digital (A/D) conversion is happening. Inside a computer is not a good place and the default hardware supplied i.e. sound cards are not great really. An external audio interface is really best, see e.g. https://www.sweetwater.com/insync/audio-interface-buying-guide/ . I bought an 8-channel one (Presonus) which sits in my home studio for live recording though if you only need 2 channels, these exist and are cheaper.
3. Software to record into. I use Reaper which is free for the evaluation version, or just $60 for the full version. I record then export (render) as .wav files (full CD quality) which can also be downgraded to .mp3 if you do not mind the drop in audio quality or that is what somebody wants. (To convert .wav to .mp3 I use Audacity which is free). Audacity might serve as the recording software too, I'm not sure (I use Reaper for its multi-track capabilities as needed).
So my take home message would be, cheap and/or convenient is not necessarily best, ideally you may wish to care about optimizing the sound quality especially at the input stage/s. I have been given "CD-ised" versions of LPs by well meaning friends which are basically painful to listen to and are considerably worse than the LPs they came from. Ideally the CD or other digitized files should be the best possible representation of the original vinyl or cassette if that is what you will be keeping and preferentially playing in the future.
I have also come to the conclusion that it is not always worth digitizing LPs or pre-recorded cassettes if they have been since re-released on CD since: even if CDs are less purist to the analogue freak, they are (or should be) a generation closer to the original master and LPs (especially if a little old) do suffer from clicks and pops as well as increased distortion as the arm tracks towards the middle of the record (where the linear speed is a lot slower), so for stuff I like that is readily available I just re-purchase it on CD these days (does not apply to all material, I know), or just enjoy the vinyl.
The cassettes I transfer are generally live recordings not commercially available; other stuff sounds a LOT better on CD (even cheap second hand copies) if available, since cassette always struggled to be a truly hi-fi medium in the first place.
Basically with a CD re-release of material previously on vinyl or cassette, someone else (with access to much more expensive gear than a non-professional) has already done the transfer direct from the original master tape, so the result *should* be better than a home user can do based on an imperfect intermediate medium (I know there are exceptions to this as well).
OK, the above thoughts come from someone with a long-term if fairly modest interest in the hi-fi aspects of recorded audio (also have recorded my own music on the system/s mentioned above, for which the planet is not noticeably any better) and may or may not be applicable to others, but I thought might be worth chipping in just in case...
Regards to all - Tony