I do pick out a horse's hooves without him being tied or even a lead/halter on, (like out in the pasture), but only when I know the horse has no issues with their feet being touched. you can start picking up your horse's feet at all times, just whenever you want to and you don't ahve to pick them all up. just pick it up, hold it, look at it, and then lay it down.
you want to have the horse allow YOU to place the hoof down, not have him pull it out of your hand. you can work on one hoof, get him to allow you to lift, hold, and slowly replace, then tell him he's good, a little pet, then lift it back up and redo. when he's good, then just pet him and stand, walk off a bit, and do again. real casual like. he should be ready and willing for you to handle his feet anywhere, anytime.
I thought you got some good info on training them to handle ropes and such, too, but if you don't feel ok about that stuff (seeing as how you are new to horses) then dont' try to be fancy about it.
Also, be VERY careful about not putting your face right OVER his hoof. never. if he lifts it higher, he can crack you in the face and break your facial bones. also, don't put your face OVER his knee when you hold up his bent leg, he can lift that bent leg higher, and get your face that way. don't put your foot right where he is likely to put his foot, if he pulls it out of your hands and puts it down real fast. Always give your horse ONE step worth of distance from his feet to yours, at a bare minimum. and know, that if he needs to move, he WILL, so don't be in that place he's going to move, shoud something spook him.