Replace the chain first, if it still slips replace the cassette. You can buy a lockring removing tool and a chainwhip and take off the cassette. You don't need the chainwhip to install a new cassette. Or you can just take the wheel itself to your LBS and have them replace the cassette if the new chain does not fix the problem. You will need a chain tool to cut off a couple of links. Cut the chain to the same length as you old chain.
On occasion, when I have broken down on the road and called my wife. We could get my bike in her car (compact) if I took off the wheels. Just be careful of grease. Frame in truck, wheels on back floor. If you don't feel comfortable about doing the work yourself...
Hope this helps.