You really have three choices, one is to try and write transactional functionality on top of a non-transactional database. As log as your transactions are very simple, and the system will be under light load, this may work, but it will likely be much more work than you realize.
You can try the alpha versions of MySQL which have some simple transaction ability built in.
Lastly, you can install a transactional database like postgres, then all you do is:
begin;
update table1 set field1='value';
update table2 set field2='value';
update table3 set id=435;
end;
If you need to handle a lot of transactions, do it in a different database than MySQL.
