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You can run the front-end on one server and the back-end on another (and communicate via JSON-RPC over HTTPS). That's how I'm able to run the Faucet and ClearCoin on Google's App Engine (they talk with bitcoind processes running on linode.com and aws.amazon.com servers). bitcoind doesn't take much memory, bandwidth, or CPU (just don't turn on coin generation), so, for now, anyway, you can even use an Amazon "micro" server (which costs something like $100 per year).
I'm not selling anything so can't comment on the shopping cart interfaces. Screen-scraping web pages is a bad idea for lots of reasons.