Most small dogs take as much looking after as a large one.
As for health problems, Jack Russells can suffer from luxating patellas, lens luxation, heart problems in fact most problems.
There are very few dogs that don't have any problems, so it is a case of choosing a breed you like the look of and then finding out about it. Decide whether you want a long or short coat, how small, lapdog or hardy companion, long legged or short, prepared to groom or pay to have groomed, so have a look at a few breeds and then investigate whether they have any problems.