turntable choice

The U-Turn is a better-built turntable than the entry-level Pro-Jects and Music Halls. 

That said, assuming a max budget of $400, you're better off getting a vintage direct-drive table from the likes of Pioneer, Yamaha, Technics, Denon or Micro Seiki. A nice example will set you back between 2 or 3 hundred. They will outperform nearly all entry-level belt-drive tables IME. Join the Vinyl Engine.com forum so you can research the model and read reviews. If buying online, just make sure the seller has experience in safe shipping of turntables (removal of platter from table, removal of counterweight from tonearm, securing of tonearm etc.)

For a good, inexpensive cartridge, I like the Sumiko Pearl. It doesn't have any huge shortcomings, is neutral in tone, and mates well with a wide variety of tonearms.

For an inexpensive preamp, one can do a lot worse than the ART DJ Pre. Better yet, search for a pre-owned or closeout Parasound Z-Phono.
 

For phono stage I just bought the NAD  375 that plugs into my amp the NAD 356. Thanks for all suggestions. 

In 2013 I went to an audio store to audition some speakers. I took along a recent MoFi Sinatra remaster/reissue. The store's LP playback system was a Pro-Ject Carbon (before the "DC" improvement) played through Naim electronics (phono stage and integrated amp). I was mightily impressed with the sound. I'm sure the electronics had something to do with it, but the Pro-Ject was up to the task and the Naim electronics showed it at its best.

Soon afterword, an audiobuddy told me he was in the market for a better (budget) turntable and I recommended the Pro-Ject Carbon. He bought the upgraded Carbon DC version and was really happy with the results.

Pro-ject Debut Carbon Esprit at $599 including cartridge is high performance /$ on the modest end!

I agree:
2. With respect to your budget $400 is too low. I would continue to save and get that budget up a bit higher because you need a few things:
1. a turntable
2. a cartridge 
3. a stylus brush 
4. a record brush
5. a phono preamp (either separate or built in to the turntable. I recommend the former as it can be upgraded and usually is of better quality)
6. phono cables and a ground cable

3. Concur with U-Turn Audio as a good entry level option.
4. You may have to wait a bit more, but Schiit is going to be coming out with their Sol turntable which as per the rear of the gear, will likely be good bang for the buck. 
Good luck!