Well, as far as running 18's and 20's you can probably get away with it, but you need to be careful with a couple of things. First would be tire width clearance, another would be tire height clearance. Measure your existing tire/rim combo to see if you have sufficient clearance. Also need to know the width of your rim, because that will dictate your available tire widths. You may need to adjust your tire's aspect ratio to get a good fit.
Let's say you currently have P275 R 60 x15 tires on an 8.5 rim and your tire is 28 inches high and fits your wheel well nicely. So you would want to stay at the or about the 28" size and move to a 20 inch rim. So to stay within these limits you would have to probably drop your tire size to a 255/35ZR 20 to get a good fit on an 8.5 width wheel. Rubber band tires.
You need to take into consideration a number of factors including available space with in fenders, back spacing, rim width, etc. But you should be able to use both the 18 and 20. Bring money. Rims and tires in that category are not cheap.
Also if your 34 is a fenderless car, ignore all of the above and just go buy what you like.
BFG has tire charts on their site, to allow you to determine what is available based on wheel size, rim width, height, tire sizes, etc. I always refer to their charts when replacing tires and wheels.