OK - basically every town in the Dolomites is a good base.
I'd recommend Campitello di Fassa OR Canazei, both located in the Val di Fassa (Fassa Valley). Pensions start at 25€ B&B and vacation homes start at 300€/week for 3 persons.
Have a look here:
Tickets: Contrary to the US/CAN, discounts on lift tickets kick in from the 2nd day. A 7 day pass for example costs only 70% of what 7 single day tickets would cost. No other way of getting real discounts, though, unless you buy a complete package.
Time: If you go between the 10th of January and the beginning of February, it will be significantly cheaper.