Short answer : you can do the change of registered keeper & order the new v5 registration papers online at gov.uk, takes a few mins but you can do it on the spot. tax too. You should still get the physical 'new keeper' part of the V5 from the seller which gives you the ref number to tax it.
Insurance you can often still setup a full policy for the same/next day and can likely get quotes online, but you will probably still have to talk to them on the phone and got through some queries to get started. Some people myself included do like to take out a temp/day insurance policy just to get a car home quick without sitting on the phone, but they can often be picky about your age and driving time.
Deffo see what the insurance will cost before buying anything, check the MOT history and whatever service records are offered.