You ask a good question. I think making a one step up to get the most out of the rest of your equipment makes sense.
If you buy a new turntable, preferably from a dealer, or in the case of VPI diect. You should receive it all ready to go and not need to touch it for at least 2,000 hours. So, what is that 3,000 albums.
To that end, i would look in the $5K range. This gets you into the audiophile range. I find that massive tables like the non-direct drive VPI are dead quiet with awesome bass and have a pretty low cost to sound quality ratio. Tables like Rega and Linn are more lively sounding. One of the advantages of Linn is you can get one in the $4K range fully equipped with cartridge or can upgrade one or two parts when you initially buy it, and then in the future upgrade all the way to their top of the line, one component at a time. But it is best to have a dealer assemble. On the other hand, if the cartridge is already mounted a turntable like VPI Prime and Aries are incredibly simple and are unsprung so there are no adjustments.
I do not fiddle with turntables. I am a klutz and impatient. I buy from dealers. They set it up and make sure it is optimally performing and that is it.
For reference, here were last years recommended turntables from Stereophile. Lots are really expensive, but many of them offer more budget oriented options.