I always use halide free, rosin based flux. Though rosin smoke isn't great for health, halides are worse. Also, in my experience, rosin fumes seem "sticky" by nature and that makes them easy to filter from the air, as they readily adhere to filter media. Just make sure that filter media isn't your lungs.
Back to the topic at hand, my favorite solder is Kester 44 60/40, 66 core, 0.031". That is "44" flux (activated rosin) which is very good at dealing with not-so-new surfaces, 60% Pb 40% Sn alloy, 66 core which means that the flux core in the wire is approximately 66% of the width of the wire, or about 3.3% by weight (58 core is 2.2%wt, and 50 core is 1.1%wt flux content). The diameter of 0.031" (0.8 mm) I feel is a good general purpose size. It is not so small that you need to feed many inches to tin a thick wire, but also small enough for any through hole and some SMD work. I also use 0.020" (0.5 mm) and as small as 0.010" (0.25 mm) for SMD. I have some Kester 44 62/36/2 (2% silver) in 0.020" size which I use where I want the better conductivity or on anything I know has silver in it. This is available at Arrow in a "pocket pak" for less than $3 (part# 83-7145-0415), which is actually a good price since a 1 lb roll is well over $100. The small spool of similar stuff at Radio Shack is a similar price/weight, but I don't know who the OEM is, and I've never used that. Comparing the MSDS sheet to that of various manufacturers might reveal the secret.