You've got a good number of replies on this; all good information. Yes, always use a drinking vessel of some sort (glass is of course preferred---most homebrews pour better in order of: glass/ceramic, metal, plastic, styrofoam--if you like 'head' on your beer, try pouring homebrew into styrofoam, chuckle.........NOT!). Eventually, when you get into it, you'll perhaps even stock different glassware for different styles of beer. But that's pretty 'into it' hahaha.
Yeast sediment, yes: remainder of the chemistry process of the carbonation. Yeast cells and such. Some brews are better with the sediment swirled and tossed into your glass after pouring about 1/2 or 3/4 of your beer---see: Hoegaarden/hefeweizen/etc.
I rarely drink it on purpose unless I'm looking for the cloudiness or extra taste/texture. And I'm still here to type about it.
But, yes, as a first-timer (and even as a long-timer) pour till you get to the bottom and then RINSE YOUR BOTTLES RIGHT AWAY, store them upside down, and you're on your way to your next batch.
May you find a first batch that tantalizes your tastebuds. Welcome to the club.