I like to wrap from the head to the base, I stretch my penis and hold it with one hand, pin the start of the bandage on the lower half of my head with that same hand and use the other hand to wrap it downward and back up again.
I don't even use that much bandage but if I just re-do it every hour or 2 it works perfectly. (it's a medium stretch bandage)
At night is a different story tho, I use a different bandage that stretches alot more in the lightest way I can to keep my dick stretched and while I can get erections with it on I'm concerned it's preventing my nightly erections from happening properly.
About the stick I don't think it matters that it's straight (the bandage does seem to keep it pretty straight tho) and I stay almost fully stretched with it on (I'll lose a cm of stretch max) but I'm sure it'd be ok to use a stick if you feel it helps you.