The difference between a garden that pays for itself and one that does not usually comes down to a handful of choices made at the start.
The most effective way to save money is to start with a garden you can actually look after.
Raised beds are popular, but they are also the most expensive way to start, because you pay twice: once for the frame and again for the soil to fill it.
Instead of renting a sod cutter or buying weed barrier fabric, lay plain cardboard over the grass where you want the bed, wet it, and cover it with compost or mulch.
Seeds are by far the cheapest way to get plants.
Compost is one of the biggest recurring garden costs, and one of the easiest to replace for free.
Mulch saves water and weeding, but bagged mulch adds up.
Step-by-step advice, charts and free garden calculators at Garden Voila.