The actual size of the tool isn't real important for starting out. You'll develop preferences for some over others as you go. The main criteria is that the tools are HSS (high speed steel). Anything else will be frustrating and short lived.
Just about anyone's brand is fine as long as it is HSS. Woodcraft has their own label tools that are usually cheaper than the comparable Sorby that they sell. The difference is in the handle, and sometimes in the length of steel in the tool itself. They are excellent tools for a better price. Some places, like Craft Supplies sell Henry Taylor tools unhandled. These are nice for putting your own handles on, but they only give you about $5.00 off for no handle.
I'm not familiar with Carlo's tools (Jesada), as I had most of mine by the time he got into selling turning equipment (brag note here). If you notice the pens in his catalog, they are my work. I consulted with him last year about this time, and set him up with all the equipment he needed to sell pens. Part of that was making the samples for catalog pictures.
You are right to stay away from sets. The lower tool prices actually become higher once you discover that you never use some of them. Buy what you need when you need it and soon you'll have a nice collection.
3/4" is what I have, but that is because it is what the store had. 1" or 1 1/4" work well too, and the size of the lathe does not dictate the size of the tool. Bigger tools will tend to bog down a smaller motor though if you try to hog off too much wood in one cut.
For general turning, anything between 3/4" and 1 1/4" is fine, either oval or regular. Each has its advantages over the other. The oval is much easier to move along the tool rest and control while rolling it. The regular skew has the advantage of greater mass, which means more stability, which means less chatter and a smoother cut. Smaller (or larger) tools can come later as you develop style and technique.
If you buy a regular skew, take a stone and just break the edges along the length of the tool. If not, you'll find that the sharp hard edge of the HSS is making a mess of the relatively soft cast iron of the tool rest.
A 1/2" gouge is fine for most work. I also have a 3/8" and a 1/4" that I use when I need something for close in work.
3/16" is ideal for most parting off situations. I also have one that is 1/16" with a real wide blade for certain applications, but I did just fine without it for years. The diamond shape is nice because you can wiggle it slightly without catching or burning the sides of the tool. I have a miniature parting tool with straight sides that I used for a class I taught at Woodcraft. After one guy used it, the whole tip was blue.
1/4" is the best to start with. A good friend of mine told me to buy one, wear it down to nothing, buy another, wear it down to nothing, and then I'd be ready for a bigger one. I already have a bigger one, but that is because I didn't want to have two of the same size.
I have a 1/2" round nose, a 1/2" square, and a 1 1/4" round nose. They are great for cleaning up grain that just won't cooperate.