well, afterwards you do whatever the hell you want or need to do, rooting just gives you administrative access and custom recovery well that gives you a recovery that actually recovers stuff unlike the stock one. past that its all up to you and your wants and needs, you want to do some sort of wifi tether program, might need root, want to customize the rom, will need root, dont need to do any of that stuff, dont need root, but having it wont hurt unless you do something silly and give the wrong program superuser privlidges
basically, after you root and install a custom recovery, make a backup, what you do from there is up to you, my only advice is, if you dont know what youre doing, you probably shouldnt be doing it. not saying be afraid to experiment within certain limits but know that you have a good backup and that the recovery/bootloader partitions wont get damaged in the process, anything you do to system or boot wont matter really as long as it doesnt spill over into the stuff that loads recovery or destroy your backup
as far as speeding up the phone, factory reset would do that, you have a bunch of apps in the background yea its gonne get slow and you dont need root for that, just uninstall them, but theres also things like boost zone, that annoying ass crap that is of little use to anyone, you can get rid of that and a number of other programs built into the phone to free up some memory but most of it is probably due to things youve installed and the only way youre gonna fix that is uninstalling some of the programs youve put on there since you got it and maybe resetting some things
now, that being said, if you can deal with a bit of glitching, the loss of bluetooth a2dp, the loss of wifi but the gain of wired usb tether, and a few other small things, i recommend the cyanogenmod port 1mouse3 and i put out, alot faster than stock but it has its issues
