The cheap stuff off of eBay, Aliexpress, ... is absolutely awful. Adding quality flux helps, but it's still not that wonderful IMHO. Also beware that name brands on these sites are likely counterfeits (Hakko, Goot, and Amtech are highly counterfeited for example).
As a general rule, stick to name brands, such as Chemtronics, Techspray, MG Chemicals, Loctite/Multicore (Henkel) for example (not all inclusive). And the easiest way to avoid counterfeits, is to buy from authorized distributors. You'll pay a bit more as it's genuine, but it's worth it (i.e. you get what you pay for). Sounds counter-intuitive, but it's actually cheaper in the long run, and you get the added bonus of avoiding the aggravation associated with cheap crap.
Personally, I've stuck to Chemtronics for years (best I've ever used). As per sizes, I use mostly #3 & 5 for thru-hole, followed by #2 for SMD.
If you don't already have one, one of those spring loaded solder suckers can be handy as well (good at getting the bulk of the molten solder off).