One more tool needs to be discussed before I launch into the actual geometric constructions. The compass. The compass is a certain type of divider where one leg of the divider is replaced with a drawing instrument, typically a pencil.
Like with dividers, you want a compass that is easy to adjust and that will hold that adjustment. General Tools distributes a compass that is inexpensive and quite serviceable. It is great for practicing constructions on paper and for keeping at the bench. This is what I would recommend you acquire first and it will fulfill most of your needs. Later you can add a set of 6″ carpenters dividers to your tool kit. With this type of divider one or both metal point legs can be removed and replaced with a pencil or a different style leg. New prices for carpenters dividers can be pretty high so check Ebay and other sources for a used pair. Ones with the metal leg missing usually are the least expensive and your going to stick a pencil in there anyway.
Always, always, always keep the pencil point in your compass sharp. A dull pencil will lay down a ‘fat’ line and lead to inaccuracies in your layouts. One last thing. KEEP THE PENCIL POINT IN YOUR COMPASS SHARP!