Every home should have a good toolkit, however, it is not necessary to go out and buy it all at once.  Investing in good quality tools right from the outset will serve you well in the long run. 

Your basic toolkit should consist of the following:

Torch

Set of good screwdrivers

Adjustable spanner

Claw hammer - to hammer in nails and get them out again

Combination pliers 

Craft knife for precision cutting and useful for general cutting around the house too

Chisel

Spirit Level

Panel Saw

A multi-compartment box with different types of nails, screws, panel pins,  plugs, etc.

Insulation tape

Fuses

Tape measure

Gloves

Dust Mask

Safety glasses

Stepladder

Toolbox

When you can, the next item to get would be a cordless electric drill with drill and driver bits.

A workbench is a useful item to have in the garage.