Yep, yep, yep, as alluded to by Massive, mastering for vinyl meant addressing certain frequencies for playback reasons - some of them physical and all related to the medium and playback devices.
It was a common problem so a standard EQ setting (RIAA?) was devised and agreed upon for that basic part of mastering and playback. Phono preamps almost universally contained the reverse, more or less, of the EQing for vinyl.
The phono EQing was forgotten by some companies when they rushed to put out CDs of their back catalogue - master tapes prepared for vinyl were used directly for CD. The results weren't very good as you'd imagine. Mind you a few of the 1st albums mastered for CD weren't much better - the learning curve still goes on.
Find MEs who's work you've heard.
Find MEs and find hear their work.
Talk to the people who've used the MEs' services.
Contact the MEs and ask if they're prepared to do a demonstration run on a track for you (lots will - thosew with longterm,
stellar reputations don't really need to).
Do they stem master or just stereo master or both?
Balance what you've gleaned with your budget.
I had some mastering done. I did all of what I suggest & it certainly worked for me.
Comparing versions of a song mastered by 2 diff MEs was very instructive & demonstrated the creativity taht's available within the scope of their services.