The only difficult part about the bb is the fixed cup, you really need a special tool to get it out and you have to be sure which way to turn it, most are left hand thread but some are RHT. For the headset cups and race you really don't need a special tool to remove. You can use a long screwdriver and hammer to tap out the cups, just go slowly around the inside of each cup, same thing with the fork race.
Once the bike is done, you want a bike shop to face the bb and headtube. They will machine the ends of the BB and HT to get all the paint off of it and more importantly, to make sure both faces are perfectly parallel. If you have them do the facing, they will likely include reinstalling the headset cups and race and bb fixed cup in the price.
Give it a try!