This question gets discussed every few months. Do a search and read those threads. (This is always good advice before asking questions on forums, by the way.)
There isn't any real change in the solder market, so it's always the same advice: Avoid cheap chinese solder like the plague, and buy a roll of "expensive" brand-name solder (Kester, Multicore/Loctite, MG, Indium, Felder, Stannol, etc.). Depending on where you live, some brands will be way more expensive than others, so don't get stuck on a specific brand, but rather choose whichever high-quality solder brand is cheapest where you live. (Tip for beginners: Don't get solder wire with water-soluble flux, even if it's on sale. Go for rosin or no-clean.)
The ideal diameter varies depending on application and personal taste, but most people like something around 0.5-0.7mm diameter (0.02-0.03"). A roll lasts a LONG time so even "expensive" solder is a negligible expense. And some added flux (like a liquid flux pen or some gel flux) never hurts. Again, don't buy Chinese crap.