You should be able to do very well for $3,000, and you should take into consideration that you are going to need content.
I suggest that you consider a used deck. Last year I bought a used Rega P7 ($2,695 new) with a Benz Micro Glider MC cart ($1,200 new) for less than $1,800. I just bought a used Sota Star Sapphire vacuum platter turntable ($3,500 new) and a vintage SME 3009 tonearm (about $550) for the same money.
I cannot comment on the Sota yet because I am waiting to take delivery, but I can say that they are very highly regarded here. The Regas are not so well regarded but after owning one for a year I don't understand why. My P7 turntable, RB700 tonearm, and Benz cart made some wonderous music and I got a lot of hours of listening pleasure out of that setup. I only bought the Sota because I wanted one when I first started shopping for a vinyl rig but couldn't find one at a good price, and the opportunity to get the Rega came along and I took it...with no regrets. But recently I had a chance to get the Sota and jumped at it. Hopefully I will like it as least as much as the Rega.
Just remember that you will need a deck, a tonearm, a cartridge, and a phono preamp. Most knowledgable people here will suggest you spend most of your budget on the deck and tonearm and relatively less on the cart and phono preamp, and I think that's pretty good advice. I've done very well on Audiogon by sticking to established sellers.
--Jerome