Hi, Pipo. Is the $1500 budget for the integrated amp only, or total (TT, amp, speakers, etc.)? I think if you get Marantz PM7001, you'd do nicely for a while... it has a phono stage. You can look for one used on Audiogon. You can also look for a used Exposure 2010S for under a grand. Also, look for a used Plinius 8150 for around $1K or less; fantastic integrated amp with tons of power & burnished, golden sound, with phono input. Many believe these are actually better than the current Plinius integrated amps made now...

I second the call on the Marantz PM7001 IF your budget is $1500 for the whole system (I have a PM7001). If it is $1500 for the integrated amp alone, I'd recommend getting an external phono stage+integrated amp.

Second that. A nice 'budget' external phono amp is the parasound Zphono. You can often get a factory rebuild for around $130.

Ok, since you're starting from scratch with $1500, and you need:

(1) Speakers
(2) integrated amp (and maybe a separate phono pre)
(3) Turntable ("TT")
(4) and cartridge (don't forget to budget for this, it may or may not come separate from the TT)

I'm not well versed in speakers, so someone else will have to recommend. But you should get these first (before the amp anyway). Decide whether you want bookshelf speakers (and you'll want to budget for stands - although you can get by pretty cheap at first if you're creative), or floorstanders. This will depend on space and taste. For that budget, I'd try to spend $500 on speakers. I'd be willing to get used ones as well.

Next, the integrated amp. I am very happy with the Marantz PM7001. The Onkyo A-9555 has gotten fantastic reviews as well, and is also in your price range (maybe a little cheaper than the Marantz) and also has a phono pre. To be honest, I wasn't overjoyed with the integrated phono preamp, and this probably is true of any budget integrated amp with a phono stage built in. You can get the Bellari VP-29 for under $100 or the Zphono that JIMV mentioned. Either of those will likely be better than the one inside the integrated. You can always just go with the internal one for now and decide to upgrade later. That's what I did. I found my Marantz for about $480. So let's say $500.

Now for the TT. The Rega P1 is a solid choice, as well as the ones you mentioned from Pro-Ject. At this price point, you'll be happy with either, I believe, and at just under $400 with a cartridge, they're a good deal.

Cables - at your budget, you can grab some 14 guage radioshack cable or order some cable from bluejeanscable.com (my choice), and cable the whole system for less than $100.

That leave you some money to buy records, something like a Shure stylus force guage and a record brush, or a phono preamp if you decide you aren't happy with the integrated one.

There are some people who are brilliant when it comes to speakers - hopefully they'll jump in.

A nice deal on a turntable is a Thorens with cartridge from Audio Advisor...they frequently have deals going so a call to them is worth the time.