[jp11801]

There are many variables in vinyl transfer and to move up from what you have may involve anywhere from $500 to $5000 depending on what table, cart, phono pre and software you use.

I would not transfer to mp3, I have used audacity ( a free program) that is great particularly for the price. I now use wave editor and peak LE but the combo is $175 ish.
If you can transfer them to FLAC or ALAC or better yet WAV or AIFF that is more ideal.

As far as a step up table wise, a good direct drive table from the 80s like the sony psx6 or 7 or psx 500-800 tables are great as are the technics 1200. This plus an entry level phono pre (think $200 ish here) will set upi back $300-500 table dependent. If you need a cart my strong recommendation in the under $100 segment is the black pearl from sumiko.

I used a set up slightly upgrade from that and did wonderful transfers. I have taken a massive step up and so have my transfers but at the level I described you can do wonderful transfers.