...ability to keep them balanced? I am needing to replace my tires soon and was thinking of buying larger tires and wheels (18-20") but someone told me that you can't keep them balanced as well as the stock wheels. Is that true?

No it's not true. Make sure that you purchase good tires like Michelin and have them installed by a reputable tire/wheel dealer.

As long as the wheels are new and not damaged there should be no problems

If you mean balancing tires, all tires are easily balanced by a machine, but to keep the car's performance the same, you need to ask an engineer or do he math yourself to calculate the right sizes, but balancing tires is simple and doesn't matter what tires they are. Balancing just makes them roll in a straight line with no wobble.