As far as gear goes, I wouldn't recommend buying any gear at all, other than your mask, fins, and wetsuit. I would recommend renting everything until you figure out what you like and don't like about gear. Try everything out first, and then buy later after your've fallen in love with something.
Practicing... Now you're talking! That's the right thing to do at this stage in your diving... Practice. And yes, a pool is an ideal environment to practice.
I would recommend practicing DIVING. Do it until you're bored. Go through two or three or four tanks just exploring your pool. When you can't stand the boredom any more, practice flooding your mask and clearing it. When you've mastered that, practice removing it altogether. When you've mastered that, practice removing it and leaving it somewhere, then forcing yourself to find it, blind.
Practice an "out of air." Remove the reg from your mouth. Don't forget to blow bubbles the whole time your reg is removed! When you've done that, practice reaching back and finding your tank valve (while you're wearing the BC - don't take it off) and turning it off and breathing your reg down. When you've hit bottom, practice turning your reg back on again. Can't reach your valve? Figure out what you have to do to reach it.
Of course, practice this in very shallow water - but master the skill and you'll be radically better off.
Try ditching your weights. Try removing your BC and putting it back on again, underwater.
When all is said and done, follow the recommended procedure for proper weighting. Lose the weight that you don't need. Take note of how much weight you really require. Try moving it around on your body, too (not just in the weight pouches - many BC's have "trim weight" pockets) in order to "balance" yourself underwater and get into a horizontal position.
Try different kick styles. Try diving with your hands folded. Try sitting completely still midway in the water column. Try doing this and breathing slightly to rise and exhaling slightly to fall.
Try convincing yourself that the bottom of your pool is filled with live crocodiles, and that touching it would be lethal. Now fold your hands and descend horizontally without touching the bottom. Without kicking, rise using only your lungs. (Remember NEVER to hold your breath, but it's okay to inhale to rise as long as you don't close your throat and actually hold it.) Then try folding your hands AND ankles and doing it again - without manipulating the BC.
Give these skills all a try - master them, and you'll be light years ahead of your class.