I have a 22hp compact tractor and use a disk harrow followed by a chain harrow.
If the soil is damp, a small disk harrow works well. The soil will lift and produce a good condition for planting. The harrow will also leave any weeds loose on the surface so they can be removed. Alternatively, if you harrow several times over - say - 2-3 weeks, the majority of the grass and weeds will rot down in the soil.
However, any deep rooted weeds like dandelions, thistles or ragwort will just be broken to produce several plants where there was only one.
The loosened soil can then be gone over with a chain harrow to produce a reasonably level surface.
If the land is dry, the disk harrow will just skip over the surface. This does reduce the weed population a bit but not by much.
Harrows work best if the tractor is driven at a fast walking pace. The speed of the harrow acts like a chisel on the soil producing a greater effect than going slowly. However, it is only going to turn over the top 2-3 inches or so. If you want to go deeper, you need a plough or cultivator. The latter could be one of the little machines you walk behind but you can get something similar to go on the back of the tractor. Using one is a slower process but the soil is dug deeper.
It partly depends on what you want to grow, the type of soil you have (light, sandy, well drained or heavy clay and so on) and what you can find at an affordable price. Even a small disk harrow or cultivator is going to be around £1,000 new. If you can find either second hand at a reasonable price, then you have your answer.
If you are only going to do this preparation once, it may be cheaper to get a neighbouring farmer to do the work for you. He will have bigger equipment and will charge you less than the cost of buying equipment that you will only use once or rarely.
NN