The Opnext HL63603TG has treated me well. Mine puts out 185mW at 300mA and is pretty bright, more so than 650/660nm despite the latter being higher power. DTR sells them with driver attached and current preset, with leads, and a nice lens if you want one. For a first build, assuming your experience with electronics is limited (as mine is), these units are great. It's a good way to get used to soldering things, and putting things together in the right order.
As to the host, the C6 is easy to work with and you can get them from Survival Lasers. You'll want the host, a heatsink (copper or aluminum are both fine), a battery contact board, and a good-quality 18650 battery.
SL's battery contact boards work just fine if your hands are steady but watch out for all the exposed metal on them – you just need to avoid accidentally bridging battery positive and ground on it and causing a short. Just go slow and be careful. You can use electrical tape as makeshift solder mask to avoid shorting it out. Flaminpyro sells boards that are easier to work with, in the event your hands are shaky (like mine) and/or you don't want to bother with tape.
The HL63603TG has a nice dot profile, even with the G2 lens. It's my "every-day carry" laser, I take it pretty much everywhere. I have no idea what the duty cycle is – the laser doesn't seem to heat up even if I run it for 10+ minutes straight. It heats up more from my hands than from the diode, even at 300mA as it is. Your mileage may vary.
Those are my thoughts on the matter, good luck and safe (and happy) lasing.