Newbie question-- where to throw my frogskins next?

Here are 2 very good turntables. The Shure cartridge on the Dual is a score in itself, although the styli are getting expensive. The Linn is just sweet with a great tonearm, although I recommend looking for a Basik if you can find one. The Axis power supplied can go bad.
Then you have money for a nice cartridge, phono preamp, maybe a cable upgrade (don't get carried away with cables. Music Direct is having a sale on the Moon pre by Simaudio: https://www.musicdirect.com/phono-preamps/simaudio-moon-110lp-mmmc-phono-preamp-amoon110lpslv

http://www.ebay.com/itm/Vintage-United-Audio-Dual-Turntable-1229Q-w-Shure-Cartridge-Dust-Cover-WORKS...

http://www.ebay.com/itm/Linn-axis-turntable-with-linn-basik-plus-tonearm-/282091203831?hash=item41ad...

You'll also want to budget for some kind of record cleaning system; but that's a whole other subject.

Given that you seem to be happy with your 5.1 system and are simply attempting to add vinyl as a source I would devote your expenditures toward that end. Stick with the electronics (amplification) you currently have.

Though it is easy to recommend upgrading your vinyl front end, and that would surly provide sonic benefits, the process need to be done judiciously at a  $1000 expenditure. 

First you need to ask yourself how do you like the sound you are getting from your current vinyl system and what about it do you want to improve?
   
Second, I agree that you need to budget for a vinyl cleaning system. This is the 1st thing I would do. One option is to check out the Spin Clean at  ~$80. There is a thread here regarding improving results with this system. Vinyl is a labor of love, starting with insuring clean records. There are many cleaning options, research this.

In terms of your TT, if you are happy with how it performs, I would look into two possibilities, upgrading the cartridge and getting an outboard phonostage. 
 
What cartridge is on the TT? I believe the AT95E is the standard on that model. I may be wrong.  Is it in good shape? With most TT systems sold with a cartridge a cartridge upgrade is a good place to start. Given your budget I would stick to MM cartridges. There are more budget options and they have greater compatibility with most phonostages.

There are several outboard budget ($130-$200) phono stages available. Schiit audio makes one that comes very highly regarded for $129. I believe any of them would make a sonic benefit over that supplied in your AVR. 

One last suggestion, purchase a copy of 'The Complete Guide to High End Audio" by Robert Harley. A great single source of information for anyone interested in audio.

Good luck in your audio endeavor.

A system can only be as good as its weakest link.  And for vinyl playback, the weak link would be sending the analog signals through the Marantz AVR's preamp.  And I just don't mean its phono stage either but its preamp section.  Even in so called "pure direct mode", its an afterthought.  That phono input the AVR has is just a  convenience and not for true hi fi performance.

So I disagree about a new TT/cartridge - it would all be wasted going through the AVR.  Concentrate on the weak link and getting the AVR out of the analog signal chain.  Find a nice stereo preamp with or without a phono stage because you can always add an external one.  If the pre-amp has an HT bypass feature even better.  This will allow your AVR to be integrated into your stereo system.  If it doesn't, you can still integrate by determining the Unity Gain position on your stereo preamp.  Google HT Bypass and Unity Gain to learn more.

An analog source is best kept with analog electronics. 

excellent advice everyone.  Thank you so much.  I will pursue!  I realize this is the high end of high-fi forums and I'm at the low end, but I really appreciate the guidance.  :-)