1.  Decent Soil--If you are going to put money anywhere, this is the place to do it.  Quality soil  will make a big difference in the health of your plants.

2.  Seeds or seedlings--Seeds of course are much less expensive.  You do not need to purchase new packets of seeds every year.  We save our seed packets and use them two or three years in a row.  The germination rate decreases with time but they will still work. You can also use the seeds from your own plants. 

3.  Fertilizer--Your plants need food and access to vitamins and minerals just as you do.  You don't need to buy expensive fertilizer, you can easily make your own from a variety of sources using composting and manure. 

4.  A few garden tools. You really don't need to spend much money here.  We have  accumulated a shed full of tools over the years, but for my vegetable garden we use only 5 tools on a routine basis:

Large Shovel
Small Shovel
Rake
Pruning Shears
Watering Can

You can buy used garden tools at garage sales and flea markets.  Or try using the Freecycle  network.

5.  Water--You can minimize water requirements by using a soaker hose or installing drip irrigation, it is not expensive to install and will save you on your water bill as well as weeding time.  Mulching will help  minimize water requirements as well.