How do you choose soldering iron tip size and solder wire diameter?

For this type of perfboard, the standard tip of most irons will do.

I think that your joint quality is either due to:

- wrong temperature

- wrong technique 

- not enough flux

Questions:

- What solder are you using, and what temperature is your iron set to?

- Do you use flux?

- how long do you hold the iron to the joint? How many times do you retry one joint?

Pad size and lead size dictate tip size. Your choice seem good for the job at hand. Other things to consider is tip geometry, wattage and temperature. Cleanliness or wrong flux may also affect the wetting. 

HKPhysicist said:

but my solder joints seem too fat, not as slim as theirs shown here

Show detailed photos. It's easier to advise when we know what your work looks like.

You are totally right alloy and core is important to select the other parameters.

1.  HKPhysicist  Ok  FORGET EVERYTHING YOU KNOW, THINK YOU KNOW.
2. Go to my Soldering School blogs and READ ALL POSTS! 
3. Then Download from the web NASA-STD-8739.3, NASA Training - Student Workbook for Hand Soldering, NASA Training - Photos:
4. these and more can be download from my Server http://www.nexgen-simulations.com/Library/TM.index.html  Find NASA and click on the links near line 60, There maybe others to interest to you as well. 
5. My go to solder is a Kester Sn63 flux core solder but I use smaller solders 0.031", or 0.025" why? smaller solder is easier to use, and less is better, globbing not allowed. 

Wow.. some of those components are tiny!

#2 chisel tip is the best for most circumstances.
the real fine point ones rarely work as you might expect. The tip heats to a point, but that point isnt the utmost tip. For soldering ram or real fine work, maybe, but most often Ill find the hot spot and trim the tip to the hot spot. for soldering tssop/ soic chips get the solder paste. tack the  corners with the chisel tip.

for long chips, pin headers, something with a long line of pins, tack in the first and last pins, and let the structure of the thing work to your advantage, holding the thing in place, as you work back. if not, you might find a tendency for things to shift in ways impermeable until its a pain to fix later.

through hole stuff is pretty simple. leaded solder works quite well, ROHS solder stinks, none of this stuff is particularly good for you. dont eat or drink stuff while you solder, and wash your hands  after.

I go with 0.031in flux core ROHS solder typically. I run the iron a 850 degrees Fahrenheit. which is arguably kinda hot, but when you get better at soldering, running a hotter iron will let you move faster.

I typically deposit a small bead of solder on the tip, hit the pad, and use the tip of the solder to push the liquid metal around the pad.

There are as many ways to solder as there are folks soldering, so just figure out what works for you.

Get a fan to pull fumes out of your face.
wear safety glasses. You get this liquid core solder, the center heats up fast, and may have a tendency to pop beads of molten metal out in unpredictable places.

if you get sharp icicle looking bits of solder forming when you pull the tip away, it means your iron isn't hot enough relative to your solder.

The multi tip kits are pointless, except to find the tip you are most comfortable with using. its cheaper to just find what you like, and get a few of those.

get yourself a scrub, and tip tinnier. starting out, I'd be amazed if you didn't destroy a few tips. leaving them on, dry, for long periods, exposure to corrosive fluxes, oxidation.... youll figure all that out, and how to avoid it as part of the normal learning process.

Yes, 0603 and 0805 are the limit for manual SMD soldering!

Soldering School LInk

Soldering School Part 1

NASA Training

0.031" ~= 0.8mm

0.025" ~= 0.6mm

with 0.031in flux core is about 0.8mm

850 degrees F is about 454C! Even too hot for non-lead and silver soldering wire; will burn many plastic materials!