It's the flux inside the solder that is very important for the end result when doing 'hand soldering'.
en.wikipedia.org/wiki/Solder_fluxThe soldermetals used in over the counter solder are almost always the same with just slight variances in relative quantities.
How a solderjoint turns out (shiny and flowing) and making good contact thus depends on the flux material and it's optimal melting point en the time it takes for the solder to flow.
There are many different flux types.
I would stay well away from the 'no-clean' or 'low residu' flux type and simply clean the flux residu (I use flux cleaner in spraycans with an integrated brush).
Leadfree needs different flux as leaded solder.
b.t.w. as Mark says the hairline solderjoints were only a problem in the early stages when PCB manufacturers were forced to adjust their machines to the new soldertypes.
Have had many of those 'hairtype' solderbridges a long time ago.
Haven't had one of those in years though and believe me a LOT of solderjoints pass through my fingers every day.
It's highly unlikely these hairline 'shorts' between solderpads will give problems after a few years as they are literally short circuits and the device simply doesn't work (correctly) from the beginning.
Mixing the EARLY lead-free with lead based solder, for instance when replacing parts and using leaded solder on an older leadfree board or soldering parts (the early lead-free parts tinned with lead-free solder) with 'normal' solder will most likely give all sorts of problems after a few years.
Have some silver-solder somewhere as well as special aluminum solder to solder onto aluminium (which can be done with normal solder as well with a neat trick) but never use it.
I don't believe solderjoints have a 'sound' the signal has passed through thousands of solderjoints before it reaches the ears and every manufacturer has their PCB's done with different types/circumstances e.t.c.
en.wikipedia.org/wiki/Solder#Solder_alloys shows what's out there and gives you an idea.
Mostly I order the brand 'Multicore' (mostly 309 flux) but tried Stannol and Multicomp as well.
It depends on what works best for the workflow and what one is used to.
Most people just buy 'solder wire' and slap it on there.
When done proper you will have no problems.
thickness:
I prefer 0.7 and have some 0.5mm.
Hardly use tthe 0.5 as you have to feed the solder quite 'fast' and thus prefer 0.7.
It's also easy to solder SMD with 0.7
It's the point size and soldermask on the PCB and the pre-wetting of the PCB that determines how easy that is to solder.
Don't use a very narrow tip or a wide one.
Generally I use a small 'chisel' type which works fine for me.
I also have some of the thicker solder but this is mainly for making 'tincan shielding' or soldering
large surface areas (large connectors with surfaces that handle large currents)
Soldering is an art with lots of science... see my avatar.