What sources do you have for the TV? Satellite? Bluray/DVD? Powered speakers are cheap, but you might still have to get some sort of HT Processor to handle the audio/video. It may be best just to look for an inexpensive AV Receiver and pair with some good but economical speakers. The ELAC B6 booshelf speakers (designed by Andrew Jones) have been known to be very excellent. Then pair with a used AV Receiver. You are still pushing $600-800 for this.
As far as the turntable system, one item that comes to mind is the Parasound Halo Integrated. Obviously, it is a preamp/amplifier combination, but it also has both a DAC and a phono preamp built in. The unit has a USB input for the DAC, so you can connect your computer directly to it. I think used ones typically come up for around $1600-1800. There's a new-in-box one on ebay for $1999. Just search for "parasound halo integrated". It also has an analog crossover and subwoofer output that would allow you to add a powered sub at anytime. It's very versatile.
There are other great integrateds, such as Hegel. Some of them will have a DAC built in. Almost none will have a phono preamp. You can definitely get better sound quality by having a separate DAC and phono preamp, but it can get expensive. You should probably post questions in other forums. Use the Analog forum for phono preamp questions. Use the Digital forum for DAC questions.
One DAC that comes to mind is the Gustard X20 Pro, with USB input for $869. This has been known to be a really excellent DAC for the money and will match DACs that are much more expensive.
As far as speakers, this is very personal as everyone has a different idea of what they like. I would recommend just going out and listening to different speakers to get an idea of the "kind of sound" you like. Certain brands have their own sonic signature and it will help to dial in the type of sound you are looking for. Speakers sound very different.
