While well over your price range, I agree with the recommendation for Dinotte - watch for sales on the AA-powered models; especially if you already have a charger. Get the helmet mount kit for the headlamp - allows you to point the beam where you need it (dark corners, drivers about to cross your path, etc.). A much cheaper but quite good taillight alternative is the Planet Bike Superflash (PBSF). In strobe mode, rear visibility is quite good and it comes with several mounting options for saddle bag, seatpost, and seatstays (or zip ties for a DIY helmet mount). Again, watch for sales. As we move into summer, the demand for lights falls way off. Performance Bike sells what looks like a PBSF clone that works well, too. Don't bother with cheap blinkies unless you are riding exclusively on trails - in my experience, you need something visibile from further away/against less than fully dark backgrounds to give overtaking motorists adequate warning. Depending on where you live & ride, a good reflector may be required by state law for night riding/a good idea. Hi-viz vests, leg bands, etc. may also help and don't cost/weight much.

I picked up a Planet Bike headlamp (forget the model) on an end of season close out I use as a spare with the dinotte for commuting (I don't want to rely on a single light). My non-calibrated eyeballs assess it at about 1/2 the light output of a Dinotte 200L. Works well for me as a "be seen" light, marginal for illuminating road/trail surfaces unless there's a decent amount of ambient/street lighting. YMMV - I like LOTS of light when I am riding at night; I also use the Dinotte or PB headlamps in flash mode as daytime running lights for sections of my commutes with heavier traffic.