Budget and boost are two words that don't go together. Do it once and do it properly. Check out the threads in Wayne's link above as they are very informative. Compression ratio will depend on things like flow rates and the charger's efficiency map. Lots of details in one of the Club GTI threads in the link. To be honest the savings between a supercharger and turbochager set up are pretty marginal in the grand scale of project costs. Most of the prep work (forged bits, fuels pumps upgrades, brake upgrades, injectors, etc.) and the aftermarket management set up are the same, just the power delivery at the end changes. And don't spec for low boost because you
will want to turn the boost up, at which stage you'll need to rebuild again for higher boost.
I was planning a boosted Polo project with an initial cost thought to be ~€1.5k. After further research the cost was upped to ~€3k no matter if I went for a turbo or a supercharger. The final costs may have been more depending on how well mapping and everything went. Either way it was abandoned because things like education and food were my priority

It just shows how important it is to research fully before dedicating yourself to anything.