To get an idea of the size, picture your board is 10/10 traces. You can place a 0201 resistor right over a trace and it will disappear.
An 0402 can be put on same trace without bridging the surrounding traces. So think about it. If you use these small of resistor, you don't even necessarily need to add any space to place pads!
When you order, make sure you check your units. SMD parts also come in metric. The metric 1206 is a different size. Imperial is more the standard.
Size of parts matters because of how hard it is to handle. An 0402 requires a very fine needle for the pickup, which makes it easier to clog and useless for larger parts. 0603 can use 25 gauge needle which will pick up bigger SOT23 and SMD caps and such without swapping needles as often. Regarding tweezers same problem. Smaller parts tend to be harder to get a hold of in the proper place and will much more easily stick to the tweezers wrong.
Tip: while soldering, if you get SMD part stuck to the tweezers due to flux, stick the tip of your iron to the tweezer until it falls off.
As far as IC's are concerned, for DIL I prefer SSOP as the smaller that is easily soldered to a pcb when considering IC's 14 pin and larger, and SOIC for the small 8 pin stuff (just because the SSOP get oversquare and probably best used in tape,,, which is pain). But for prototyping with veroboard/breadboard, they are evil. But when choosing between quad packs, I actually prefer QFN over QFP for packaging reasons. Trays of QFP are a PITA.
For passives, where size and dissipation doesn't matter, I tend to go 0805 for the resistors. For decoupling caps, 0603 tends to be cheaper for given voltage rating. Caps are also easier to handle because they are heavier.
Sidenote: Some 0603 resistors are marked with value. I've never seen 0402 that is marked, although I bet there are some. All 0805 and larger I have ever used have the value marked on top. This is a slight bonus when prototyping.