So out of these two kinds of solder, which do you think is better? I should get the smallest size?
Solder Brands
Though most solder will function the same assuming a rosin core and the mix, I might opt for that MG Chemicals brand as that "Delcast" isn't even showing the same brand in the pictures (it's JuFeng on the label). I doubt the Chinese are selling bunk solder, but you might as well opt for something decent as you'll be using the same solder for a very long time.
For myself, I use a 1-pound roll of Kester Flux "88" that a friend gave me, and which will last me literally forever. They don't sell that particular variety (88) anymore, but their 44 variety is just as good. The Kester has a higher flux percentage than the two brands above, at 3.3% compared to 2.2%, but I don't know if that will really make a difference. Given the cost of the Kester, and the good ratings of the MG Chemicals brand solder, the MG Chemicals solder would probably be a decent choice.
I'd opt for the 1/2 pound spool. The flux in solder has a shelf life, and even a 1/2 pound spool will last a long, long time. Still, my 1-pound of solder is quite old (almost 10 years!), but seems to function fine.
Solder Diameter
I do mostly through-hole type soldering, not SMT soldering; so I think the thickness I use (0.032") is a good general-purpose solder diameter. The thicker 0.05" varieties don't give me enough spatial control, while the smaller diameter varieties don't give me as much movement control (it bend too easily). For the smaller stuff, I also find I need to feed longer lengths into the solder joint/hole to compensate for the smaller diameter.
You can see the
size of different solder thicknesses compared to different components here (scroll down). The 0.032" strand is just about the right diameter for the pins and wires of components. That diameter has also worked fine for most of my light SMT work, especially using alternative techniques to compensate (described later).
I don't, however, solder extremely fine pitched stuff like The Lightning Stalker. The smaller diameter solder would definitely be useful for that, but you should determine how much SMT work you're going to do before buying a large quantity. For me, I don't do much of that, so a large quantity of very small diameter solder would be a liability.
Technique!
Remember, it's more about technique, and you can usually compensate for solder thickness with soldering practice and techniques. For example, the guy in the video below is using 0.5mm (0.022") solder, but it is still too thick to really do decent soldering on an SOIC. Instead, he uses flux, pretinned pads, and the solder left from a bridge to sweep the solder across the pins.
Also remember that soldering tiny leads can be just hard in general, even with thin solder strands and fine tips. It's hard to control the solder strand and your iron at those small pitches, and you'll need to rely on techniques like the above to compensate. This is another reason why I don't use super thin solder: I usually end up bridging pads anyway, so I just use other techniques to get my SMT work done.
You might want to buy a combined SMT/soldering station and have the option of just melting the solder onto the pads using the heat nozzle, or make your own reflow oven from a toaster oven and a temperature controller. That can come later though, and maybe never. Hell, I used my reflow nozzle more for cooking heat-shrink rather than SMT work.