I started changing my own tires 4 years ago, after buying a tire changer from Harbor Freight. The only time I had a problem was when my air little compressor didn't have enough punch to seat the bead on a radial tire. I have a bigger air compressor now. I covered the rim clamps with duct tape to protect the wheels. Tube tires are a piece of cake with the Harbor Freight changer. Well worth the hundred or so bucks, it's paid for it's self already.
Bike shops around here charge about $25.00 to mount and balance a tire, (if you bring them the wheel off the bike) plus a $2.00 tire disposal fee. Car shops don't seem to have a problem mounting and balance for free w/purchase.
As for balancing, Static Balance works fine. I simply put the axle back through the wheel, and put it between 2 automotive jack stands, then give it a gentle spin, and the heaviest side will be at the bottom when the wheel stops, then temporarily tape a weight to the rim at the top, then repeat until the wheel stops just about anyplace, then secure the weights.
Surely someone will chime in, and proclaim that this method is not accurate enough to be safe, and their right,
if you're doing 160mph down the back straight at Daytona! chances are your barely getting over the ton on your 40 yr old SOHC. Just keep in mind that many motorcycles were successfully road raced on static balanced tires long before computer balance machines where invented, they just used a better wheel stand than my make shift jack stands.
I've seen a many tires with a lot of weights on them, then see the balance dot nowhere near the valve stem.
That little balance dot is the lightest part of the tire's carcass, and should be located next to the valve stem, The heaviest part of the wheel. I have 3 bikes in my garage right now, and only 2 of those 6 wheels have any weights at all, and all have been well above the legal speed limit on the interstate with no problems.