^^ agreed. 60/40 or 63/37 is the way to go. Get it in a .032 size for 22awg wire and make sure it is a no clean since I assume you are going to use led stars. Do not go with a lead free. Sucks to work with, temps required are pretty high and so forth.
For a soldering iron, you can get away with a 25w iron, but a variable temp unit with chisel tip is preferred. An outstanding, digitally controlled unit with short (easy to work with) quick change tips and 15 second total warm up can be sourced for around $60. And they can be calibrated.
I have used this unit for around 7 years for literally thousands upon thousands of solder joints and it is simply amazing. I have to solder for a good part of my living so my recommendations are from a professional so no worries there. Puts many $150-$300 units to shame.
http://www.circuitspecialists.com/lead-free-soldering-station.html
I also own this unit here which is basically an update to the above and costs the same. Again, an OUTSTANDING unit that you cannot go wrong with.
http://www.circuitspecialists.com/soldering-system-bk3000lf.html
For tips for either unit, purchase an lf12d or lf16d.
If you buy one, thank me later
Also CSI has this unit out as well now but the iron itself is a junker similar to what most weller stations use. I have been meaning to try it with my quick change iron since it has 4 presets which would really come in handy! It is a 60w vs 70w but that would only translate into a possible slower total warm up time and recovery time but I doubt it would be very noticeable, again have not tried it but want to.
http://www.circuitspecialists.com/soldering-station-60-watt-3dlf.html
I use this quick change iron handle that comes with the first two irons I recommended because well... it is quick change but the really awesome part about it is that the distance from the hold point to the tip is VERY close so you can be very precise with it when it is needed. It says "for lead free" because it is rohs compliant, but soldering tin lead is perfectly fine and is not hindered by it at all.
http://www.circuitspecialists.com/b010.html
For solders, there are many, many types on the market. I have probably 25 spools here that I have tried over the years but my absolute favorites are....
- Kester 331 / water soluble flux. This stuff is AWESOME for work which will be seen. Once you finish, you run your pcb or other under DI water and scrub the flux with a toothbrush. Rinse and repeat lol. Joints will come out 100% flux free and look like chrome and stay that way. Would not use it on led stars to note but for other projects it is awesome as no chemicals are required to clean the flux. Once finished, blow out all the components or any place water can hide with compressed air.
- Kester 275 / No clean flux. Just solder and your finished. Very good wetting for hand soldering.
- MG chemicals no clean also works well, is easy to find and is cheap.