I've built quite a few bikes, including wheels too.
Tools? While not a necessity, having a workstand and a well lit area with some space is a huge advantage and makes things
much easier. It will also probably save your frame from getting at least one scratch when (not if) it does fall over if you don't have one. It's good to have an internet connection and a computer to ask for advice or research how things are done. However, like I said, both of these aren't necessities though. Other tools* you will need? Well assuming you are using pre-built wheels:
- allen keys for brake and shifter and stem/handlebar. seatpost clamp, derailleur installs
- screwdriver (more than likely needed to adjust the derailleur)
- cassette tool for tightening cassette up
- chain whip or old chain for removing a cassette (OK, if you are only building, you really don't need this)
- adjustable spanner to hold cassette/bb** tool
- chain tool assuming you aren't using a chain with some form of quick link in it
- bb tool
- pedal spanner (you can sometimes use a regular spanner for this, but usually a thinner profile pedal spanner is easier)
- starnut installer for fork assuming one isn't in there (while i'm sure you could install one with a hammer and screwdriver, for the very little cost of a starnut installer, I'd say get one)
- race setter (sometimes you can create a home made one -but don't use a hammer and a screwdriver, it's just an invitation to burr your race)***
- headset press (I have to admit I use a home made one made our of a big bolt -usable and not easy, but it's not often I install a headset so I couldn't justify spending big bucks for one).**
- cable cutters for cutting cable and housing as well as crimping nipples
Miscellaneous:
- chain lube
- bearing lube
- frame protector if you have a steel frame (why not? If it's apart, now is the time to do this!)
- anti-seize for crank/bb, crankarm/pedal interfaces
- degreaser for cleaning stuff
- rags
- good quality spoke wrench (even if you buy wheels they might be a little off, or they will be sooner or later -OK admittedly not build related)
- cable ends and nipples
- cable doughnuts (not always needed admittedly, nice to have when you do need them)
- while it shouldn't be used for an install, and depending on your crank design, a crank puller to get the arms off is good to have
- cone spanners for adjusting the wheel bearings are great to have (again, not necessarily required for an install though if your wheels are in good order)
I might have missed something, but I think that covers most of it. You can definitely save some money by getting a bike shop to do some stuff that will be cheaper than buying tools (e.g. facing, race and headset install) unless you want to do it many times over or just want to do it yourself. Concerning order, it's pretty easy -you need to have your bb installed first before cranks (obvious!) or your fork before your headset (again, obvious!). Likewise put your wheels in before adjusting brakes. Install shifters before tuning gear changes. If you use a workstand, make sure your seatpost is in early.
One last thing: yes, it's expensive to get set up, but if you do want to do it,
do not skimp on good quality tools (e.g. a poor quality spoke spanner is a waste of money -just buy a decent one in the first place!). Park Tools are usually good quality, but can be expensive (strangely my cheap pedal spanner is much better than my Park one which I think is quite poor).
*some tools differ on your components (e.g. old cranks needed c-spanners, non-headsets needed large flat spanners whereas headsets use allen keys)
**you should use a torque wrench to get correct settings (some people may disagree with this one)
***sometimes for the risks involved, its easier to pay a bike shop to do this -especially if you are going to install headsets and races very infrequently