In general, its a lot simpler if you stick with either R-12 or R-134a, because most AC places can recover and recharge both of them. R416A may work fine, but you will need to be prepared to do everything with your own equipment.
I checked an online store for the price of 30 lb cylinders of refrigerant:
R-134a - $199
R-416A - $295
R-12 - $577
This puts the cost of bulk R-134a at about $7/lb and bulk R-12 at about $21/lb. Since most systems won't need more than about 3-4 lbs of refrigerant, either choice is probably within a reasonable budget. However, I've found that most repair places don't stock R-12 anymore and may not be maintaining their R-12 recharge machine, since nearly all their business is with R-134a.