I have a 75' X 200' garden and I till it with the tractor. You could do it with a walk behind fairly easily now that it has been created and the soil is in good shape. I do my little garden with a mantis "chainsaw" (2 cycle) tiller. That garden is 25' X 50'. The soil is light and there are almost no rocks at this point. It takes so little time to do it with the small tiller there is no point in putting the big tiller on the tractor. I leave the backhoe on the tractor, and though it is easy to take on and off, it does take some time to do.
In my experience the big job is creating a new garden. I won't use herbicide in my vegetable gardens so eliminating the sod has been a big challenge in the past. If you till it in you have chopped up grass that grows back with a vengeance and you fight it all season. Every time you till you also expose new grass and weed seeds that sprout and you fight them too. What I do now is take the backhoe and cut off the sod. I find that with the FEL I tended to remove too much soil, with the backhoe I can take off just the amount of sod I want. Then I dig down 15" or so with the backhoe to loosen up the soil and remove all the rocks (I have a LOT of rocks). The tiller will only get down six to eight inches deep. When I used the tiller in the past to loosen up the soil for a new bed I thought at times it was going to bounce so hard on the rocks it would rip off the tractor. I had to till with the parking brake engaged to keep the tiller from driving the tractor forward and I bolted angle iron to the top of the tiller so I could stack cement blocks on it to add additional weight.
After the rocks are out of the new bed I till once to chop the clods up and then add compost and soil to replace the volume of rocks I’ve removed and till again. After that the tilling is almost effortless.
We have been using weed barrier fabric in the garden for the last few years and it is a great time saver. We used to fight the weeds all summer long and now a few minutes with the hoe takes care of any that sneak through the gaps in the fabric. I hated weeding corn and onions in the past because the sprouting grass looks just like them. Now I plant them through the weed barrier and forget about them until it is harvest time.
A small tiller would probably do your garden just fine. If you purchase one that is smaller then the width of your tire tracks though, be sure that you can shift it to one side to eliminate one tire track. This limits you to being able to till in only one direction in the bed but that is seldom an issue. With my
BX22 the weight of most tillers is an issue. Even most of the smallest ones are over the mfg’s stated 3pt weight limit for my tractor. You should consider that when making your purchase. Given the choice I’d buy one large enough to eliminate both tire tracks.