Hmmm. I'd be happier if you'd said $500-1,000.
A $3K rig is well above the plug 'n' play level and a used rig @ $3K would be even more so. Getting your money's worth from rigs at this level takes some hands-on experience and a climb up the learning curve.
I don't want to discourage anyone from trying (or re-trying) vinyl, but to buy a good rig, use it for a few months and then sell it may be unrealistic. I fear you'd soon be sucked into vinyl-mania and swilling snake oil like the rest of us! It's not a bad life, but it's not what you said you wanted to do either.
RIAA equalization is not related to volume level. It's related to frequency response. Unlike CDs and DVDs, music is not recorded on vinyl with flat frequency response. Before any record is cut, bass frequencies are attenuated and treble frequencies are boosted, typically on a curve defined long ago by the Recording Industry Assoc. of America. This helps the stylus track the grooves and allows longer side times. A phono stage includes the inverse of the RIAA's curve, to bring frequency response back to flat.
Volume level is another issue, which you were right to mention. The output of most phono cartridges is lower than the output of a CDP or other line level source, often much lower. Extra gain is required. Phono stages provide that too.
Many phono cables are or can be terminated with XLRs, but you won't find any decent TTs with internal phono stages. AFAIK that is available only on VERY entry level rigs. If a sub-$200 plastic toy will meet your sonic needs, by all means go for it. They're available from various mass-market e-tailers. Just don't expect much from the sound.
If you decide to proceed despite my annoying nay-saying, on a $3K budget I'd allocate roughly:
- $1,500 for table and arm (used)
- $300-500 for a cartridge (new, used is risky)
- $500-700 for a phono stage (used)
- $500 for a record cleaning machine, supplies and tools
Yes, records must be cleaned - especially for copying. If we'd all known this in 1985 CDs might never have taken off. The virtual elimination of background noise removes one of digital's two advantages. (Convenience is the other. As you can tell by now, the inconvenience of playing vinyl has yet to be reduced!)