My budget for this year (second year gardening here) is about $500, including seeds, manure, rototilling a new bed, potting soil for seed starting, etc. Not really "budget" gardening, but not as extravagant as I could be if i thought i was living here long term. So far I have spent about $350, trying to figure out where I will get the most for my remaining money. Last year was a bit more, but we bought a lot of wood chip mulch and tools. A butternut squash is about $8 in the local store right now, potatos are more than $1/lb, so although that sounds like a lot, we will get far more in produce than we put in.
Save seeds. Each year I grow from my own saved seeds, things seem to produce better. I think it has as much to do with epigenetics as genetics. A package of heirloom tomato seeds or a few starts might be $5. If I save the seed, the next year, I can grow that plant again basically for free and use the money for something else. I didn't buy any tomato seeds this year and my only commercial pepper seeds were gifts. I bought no new pepo squash or melon seeds, did add new cucumbers and maxima squash. I havent reduced the amount of money I spend on seeds yet, but have increased how much I can grow with the same budget! If I was on a tighter budget, I could have grown fewer varieties of each thing, but I am still trialing to find things that work. You dont have to buy fancy seed starting cells either. I use a lot of egg cartons, cream cartons, plastic trays, and other things scavenged from the recycling bin. Also- although i love the heirlooms and unique varieties, for things like carrots and onions, you can get 1000s of typical variety seeds for a few cents more than a few hundred
heirloom seeds at some of the big seed companies, enough to last a few years for me.
Mulch. Depending on your climate, mulch might make your gardening far easier! Water, and my willingness to water things is a bigger factor for me than soil fertility. Mulch doesn't have to be expensive. The best mulch I ever got was free used
mushroom compost from a local mushroom farm- carried home in buckets and more wrapped up in a tarp in the back of my car. It kept the soil moister, was weed free, and provided nutrients. But I also like wood chips and straw, both of which can be cheap. Manure can be picked up for free on local buy and
sell sites. I have an alert set right now until one pops up that's close enough. A truck would help, but my small car works fine. Also- I have been surprised to discover posting wanted ads works! Just got my garden rototiller from placing an ad, picked up other stuff the same way . This year I have a large bed mulched almost entirely with yard waste from the neighbors and waste cardboard collected over the winter. Completely free, unless I decide to add manure to break it down further.
Like Anita said, get good quality tools- I prefer heavy steel heads, not flimsy modern stuff. But that doesn't have to cost too much. All but my garden rake and scuffle hoe came from my grandmother or garage/estate sales and cost $5 or less- and my grandmother is after me to get a "better garden rake" as the best one I could find in the local stores ($40) has too heavy a handle and she considers it worthless. She thinks the same about my scuffle hoe! For me, a nice spade, a trowel, a garden rake, a leaf rake, a digging fork, a large and a small hoe/scuffle hoe are probably the minimum, but we do have more than that, and some duplicates. I will be looking at mail order $100 + tools to replace anything that breaks if I can't garage sale it, but my used tools work just fine.