Looking for a turntable around $1k...

I don’t and won’t have tons of $ to throw into an analog set up. I’m primarily digital and CD but I still have enough recordings that are vinyl only as well as others of sentimental value that I listen to regularly enough  that I can justify getting a decent turntable, at least at the price point I set. I know that some people have expensive opinions about turntables, but I can’t go there. 

My listening set up is a Schiit Mani phono preamp, a Decware Torii MkIV amplifier, and Omega 6.5” Alnico Junior XRS speakers if that all matters.

I’ve been using a Technics AT-LP120 for years and I have come to hate it. The tone arm is floppy and it has become pretty much impossible to lower the needle without it bouncing off the record. If someone down the block sneezes, the record skips. No matter where I place the table. Everything about it has gotten worse and I fear that the turntable is damaging my records at this point.

I’ve been considering the Rega Planar 3 but do I even need that?

Is there a sleeper turntable around $1k that I don’t know about?

Could I just get by with a Planar 1 or 2 given that vinyl is what I listen to 3rd most behind HD streaming and CD?

I've owned Regas and Thorens' in the past and could never quite optimize their set-up. If you are knowledgeable and enjoy tweaking and adjusting your turntable, they could be a good choice. A year ago I purchased a Fluance RT85 fitted with the Ortofon Blue 2M. This is a fantastic sounding turntable for the money. It minimizes adjustments and the feet provide very good isolation, so it's quiet. I've also auditioned the MoFi Studiodeck (with the matched StudioTracker cartridge) and thought that was an excellent sounding turntable and would probably be my choice to upgrade. Oh, I'm using a Schiit Mani, also an outstanding value. 
Brand new Technics SL1200 mk7 cost exactly $1000 and this is the best you can get with your budget (in my opinion). If you can expand your budget to $1800 you can even get the next GR model

This is about mk7 (and GR is even better): 

"The direct drive motor (D.D. Motor) formed the core of the SL-1200 Series. In addition to providing unparalleled accuracy, the D.D. Motor technology that was introduced in 1970 offered reliability for long-term use with its excellent durability. This further evolved with the SL-1200MK7, and achieved even higher sound quality as the Coreless Direct Drive Motor.

The SL-1200MK7 comes with a static balance S-shaped tonearm to carry on the Technics tradition. The tonearm moves in a unique arc as it tracks the record disc, and reproduces music with high fidelity. The bearing section features a high-precision bearing structure. The tonearm provides high tracking performance without stylus skipping even under hard usage.

Each insulator foot consists of an internal spring and rubber, and the bottom surface is covered with a cushion material. They effectively shut out vibration even in a loud sound environment. If the turntable cannot be set up on a perfectly level surface, its height and inclination can be adjusted by turning individual insulator feet."

As a Rega Planar 3 (newest revision) owner,
I’m settled for now. The spacer recommendation I saw earlier is likely required for many carts. An Ortofon 2M Re is not a good recommendation however. Look at a  a 2M Bronze (better engine and superior stylus shape), or a good Audio Technica in an appropriate price range. 
I have a Pioneer PLX 1000 right now with a Ort 2M Bronze that is satisfying. Bought the PLX by Stereophiles recommendation. 
Now I want to upgrade both though, and I don't listen to vinyl all that often, but I do use it for ripping to flac files.