Recommendations for a modestly priced analog system

There are several different ways of spending $5-7K for turntables (including plinth, tonearm, cartridge, headshell, tonearm cable, phono preamp).
The easiest way is to buy one as a whole package. There are cons and pros of buying the whole or separates, and buying used or new. If you are not that knowledgeable on analog systems in general and not quite techy, I would recommend you to buy a new turntable from a local store that comes with everything (except phono preamp). If I were you, I would buy something like Technics 1200GR ($1600), Rega P6 ($1600) or Clearaudio Concept with Satisfy tonearm ($2000) and spend extra $500~1000 for a new MM cartridge. And $1000 ~ $2000 for a new phono preamp. Then, spend the rest for buying albums and an ultrasonic record cleaner. 

After a few years, you might feel an urge to try different, then you might think of buying vintages (like Technics, Denon, Thorens, Garrard) and think of mono cartridges or MC cartridges and SUT.

I've owned over ten turntables (which is a modest number for Analog folks), and now I have three, one from each kind -- BD, Idler, DD.
Clearaudio Bluemotion (whole system, bought new).
Garrard 301 with two arms (bought used, all separate).
Denon DP-80 (whole system, bought used).

Again, there are many paths, and there is no one right path. 

Your Cary will have an MM stage, so unless you want to run a step up, you'll want to look/consider an MM cart.

You have TONS of great options for a table/arm and cart at that price point.  As matter of fact, you really don't need to spend that much, unless you just want to.

Couple of ideas on the new side--

VPI Prime 21 with an Ortofon 2m Black

Pure Fidelity Encore with either the TA-1000 or Origin Silver Arm plus 2m Black Cartridge

A Sota Sapphire with an Origin Live Encounter tonearm and Soundsmith Carmen cartridge will do the trick nicely.

This!  ^^ 

@millercarbon.   My preamp Cary SLP98P has a phono stage in it. But, I don't know if I should get a better one or not.

That's why I asked. A better phono stage will be huge, if you can afford it. The two that would be great with the excellent rig above would be the Herron VTPH2A at about $3600 or the Decware ZP3 at about $2k. I have the Herron, its an outstanding over-achiever, and the Decware seems to be as well.

Either of these will be a massive improvement but each with a different flavor. They both use tubes but only the Decware is all triode zero feedback, and depending on cartridge output may need a step-up. But Decware has SUT with free exchange eliminating a lot of the usual SUT hassles.

FYI....the built-in phono stage on the Cary is actually a decent stage...but as I mentioned above, is MM only.

@chungjh Your Cary SLP-98P only has 43dB gain on the phono so you won’t be able to use any carts less than ~2.0mV output w/o using a SUT. That’s pretty limiting for the otherwise $5K-$7K vinyl rig you’re considering. Another issue is that the linestage side of the Cary produces 20dB of gain which is pretty beefy and could start introducing quite a bit of noise if you start adding a separate phono pre into one of the line inputs on the Cary. Years ago I had the same pre and felt the gain was too jacked up and the unit was a bit noisy and simply not resolving enough, particularly for a higher-end vinyl setup. This may be an opportunity to swap the whole unit out for a different preamp, possibly with phono integrated. There are so many choices out there. Don’t just plug in a Herron or Decware or anything else into the Cary w/o thinking about the implications to your setup as a whole. Ignore the folks who give advice without understanding your entire rig...one size never fits all.