Don't "double up" on ANYTHING until you have some mileage under your belt. Many, many, new climbers over-buy out of eagerness early on. I would recommend:
1 set of BD Stoppers, size 4-13
The Pink, Brown, and Blue Tri-cam
A few finger-tip cams, either aliens or C3's
BD Cams .4 thru #2 or #3
8 shoulder length slings
16 biner's for above slings, I like the Petzl Ange if you go dyneema for above slings
2 quick draws
2 double length nylon slings
1 shoulder length nylon sling (for racking)
1 belay device
That's my general set-up for most anything New England. Occasionally you need something else but your route research will tell you that and by then you'll know who to borrow it from.
And since I learned from a lot of reading and some professional guides, and later became a guide, I'd suggest finding one of those as well, unless you can hook up with an awesome mentor, or squared away climbing club/group. A few days with a good guide can be well worth it...
My guiding philosophy: http://davidlottmann.wordpress.com/guiding-philosophy/