Firstly, I would say spend the money on one decent tool rather than a few cheaper ones. Please stay away from gimmick tools that claim they will not only remove nails, but can also be used to stir your tea.
But before the tools, I believe the first thing every half-decent handyman needs is a workbench with a vice.
This will ensure your dining room table does not get scratched, and you are not called in to assist as the extra pair of hands that is always needed to hold something.
Below is what I believe your toolbox should include:
* A set of screwdrivers, both flat and star.
* A claw hammer with a steel shaft.
* A set of flat spanners, a set of socket spanners and pliers, including long nose, lineman and side cutters.
* A cordless drill with a spare battery; only a good and reliable make.
* Saws. These won’t be used often, apart from a hack-saw, which does most things, I spoilt myself with a powered band saw and a table skill-saw.
* A spirit level to ensure your partner cannot complain because you did not hang something level.