For secondary/tertiary, people almost exclusively use carboys (usually glass because of the long term untested-ness of plastic carboys). They can be any size you want, though most people use 1, 3, or 5 gallon carboys. Primary's done in either a bucket or another carboy. When you reach secondary/tertiary, make sure you top up with water or somehow completely remove any head space above the level of the mead. Air exposure is bad at this point.
Mead is ready for bottling when fermentation has completely stopped (either stable SG readings for 2-3 weeks or campden tabs + potassium psorbate), the mead has been degassed (no CO2 in it), and it is clear. For degassing, you can buy an attachment that goes in a power drill and whips up the mead (releasing all the CO2), or you can just wait for ages (I think all of it is gone by month 6 or 8, but check to make sure). Clearing is achieved by racking and cold crashing. Rack every month or two to get it off the lees, and things should clear up fine. If you have trouble, cold crashing (i.e. sticking it in the fridge) will help more lees settle out. Not sure about chill haze in mead, you might wanna look into it. Fining agents can be added if you have a particularly stubborn mead that just won't clear. Once fermentation has stopped, the mead degassed, and it is clear as crystal it should be good for bottling. It will, of course, continue to improve if you let it age even after all these criteria are met, but that's up to you.
As for your last question, I'm not quite sure how to proceed in answering it. I'll agree that I don't much care for commercial mead (nor do most). About what "kind," though, I'm not quite sure what you're asking. I would recommend trying dry or semi-sweet meads, as they are more interesting and difficult to find. If you mean by "kind" a certain meadery, I find B. Nektar Meadery to produce some decent stuff.