Agreed on an integrated making ideal sense for you. Marantz is one of the few companies that still makes a budget integrated with a phono stage, and it's very decent (I owned a previous incarnation). And it has plenty of power, too--Music Direct sells it. When I was getting into this hobby at 21 I bought an NAD integrated and kept it for nearly 10 years--and I'm still using a newer NAD amp, after I regretted selling the first. You can't go wrong with a C320BEE or C325BEE (they're virtually identical) for a starter--and even keeper--though they will require an add-on phono stage. Go with NAD, Pro-Ject, or Bellari, and you're set for the phono. NAD amps tend to be a little warmer in tonal balance than the Rotel or Arcam. Jolida's tube/solid-state hybrid integrateds are great, too, but need a phono stage as well.
As far as speakers go, I can't recommend strongly enough that you listen before buying if you can. Especially in a starter setup, and given a decent TT such as you're looking at, they're likely to be the biggest factor in your daily enjoyment of your rig, with it putting out the color of sound you want to listen to. The $350 KEFs I bought at the start are still in my system. At the very least find out if you like a bright/detailed, warm/midrangey, bass-heavy/full sound, and then look for speakers that seem likely to suit your tastes (and the size of your room). That said, it's hard to go wrong with any number of decent monitors, new or used, in your price range. You'll get recs galore in the speakers forum, I'm sure.
As far as speakers go, I can't recommend strongly enough that you listen before buying if you can. Especially in a starter setup, and given a decent TT such as you're looking at, they're likely to be the biggest factor in your daily enjoyment of your rig, with it putting out the color of sound you want to listen to. The $350 KEFs I bought at the start are still in my system. At the very least find out if you like a bright/detailed, warm/midrangey, bass-heavy/full sound, and then look for speakers that seem likely to suit your tastes (and the size of your room). That said, it's hard to go wrong with any number of decent monitors, new or used, in your price range. You'll get recs galore in the speakers forum, I'm sure.