Of 3 different types, all at the budget end (£60-£90).
One daughter has a HP model (no longer available), my other daughter a Lexmark (1150) and I've just installed an Epson (CX3200) for a friend.
All offer convenience, some space saving (the HP and Lexmark the most!) and real convenience.
The Epson is the biggest, by far, but does produce good photo output and the software seemed very straightforward. It took two goes to install, but then worked fine. It can also copy without the computer being switched on, which might be useful.
The lexmarx looks pretty good, is not too big, was very cheap and has worked well. It needs the computer being on to copy. The output looks good too and it is pretty fast for B&W text. It installed first time and the software is good, although I would prefer the Epson.
Th HP has been going almost a year with no problems and was straightforward to install, is very neat and can copy without the computer being on.
Since all are colour inkjets the cartridges can be expensive if a lot of printing is done. If you only need B&W then do look at All-in-one laser printer based solutions.
Also none of the above has a 'stand alone' fax option, which you might want, in which case your budget will need to be around £130+.
With any all-in-one solution you do run the risk of any problems in one part meaning the whole assembly is useless and also, generally, the quality of an all-in-one will be less than the best single units. But many people find the advantages of ease and space outweight that.