In my opinion the cheapest one would be a c6 445nm blue build. that was my first and second one. however it will cost you a bit more than $75, here is a list of what I purchased:
Blue m140 diode in module with leads and 3 elemental lens from dtr for $68 incl shipping
aurora c6 diy host from dx $10.90
1.25A driver from dx ~$2 (you can get better ones from members here depending on your budget they will be around $10-$20 ie dtr sells some too, but if you get a higher current you will get more power and will need right heat sinking
C6 heatsink from eudaimonium $10
2 3.7V 16340 batteries and charger from ebay ~$6
and I already had glasses but if not you must get one before you build a high power burning laser
Overall the cost is less than $100 and will give you a 1W+ laser.