I can heartily second his recs on the 35mm f/1.8 G as a budget gateway to fast primes on DX. I also own and love the Tamron 60mm macro/portrait combo, and its an amazing bang for your buck, and does both portraits and macro reasonably well.
Here's my preferred DX setup: (With a 'I don't need fast glass' cheaper rec in parenthesis)
Tokina 11-16 f/2.8 (or the sigma 10-20mm if you only use it for landscape and don't need f/2.8)
Tamron 28-75 f/2.8 (or the 18-55mm kit lens if you don't need fast glass) The Tammy here is technically a FX lens, but really is better as a DX lens than an FX lens, since it's pretty weak around the edges, but the center image is really good which is all the DX sensor sees
Nikon 80-200 f/2.8 AF or if you have a non body focus motor, I guess suck it up for the 70-200 AF-S VR (Nikon 55-200 VR if you don't need speed)
Nikon 35mm f/1.8G AF-S (no non fast budget recs for the primes, as that sort of defeats the purpose of primes)
Tamron 60mm f/2 Macro
That setup will run you around $2,800 new to around $2,000 used, depending on the condition you buy. It's a REAL solid setup for a DX body. It will also give you two starter lenses if you ever decide to go FX (the 80-200 and 28-75) so you wouldn't be building an FX from scratch.