turntable choice

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!

+vintage over new in your budget way more bang for the buck. 

In the Pro-Ject line, I would not go any lower than the Debut Carbon Esprit SB. Big benefit is the built in speed box and acrylic platter. But that's a couple hundred over your budget. It's a solid entry level TT. But I found the included Ortofon 2M Red cart way too bright. When I had one, I swapped out the Ortofon for a Nagaoka MP110. So another $100 there.

$400 isn't a lot to get started with. Might be better to wait and buy a better TT, otherwise you may be upgrading it in 6 months.