"I will be reloading .223 and .270. What die sets and the best 2 die of 3 die sets? What brand is the best, LEE, RCBS, Hornady, or some other? Remember I am on a budget "
All standard die sets for bottle neck cartridges are "two die". Lee has a couple of sets with a third die, in one it's a crimper die and in the other it's a neck sizer. I doubt you will need either of those extras so stay with the two die sets.
All makers make good dies, the quality of the ammo from any of them is the equal of any others. One design may tickle the fancy of some folks, others like something else but it takes personal experience to have any idea of what YOU will like!
In your shoes, I would take the Lee dies without question. They have the least polished exteriors and the price shows it, but that doesn't hurt your ammo. Most Lee sets include a shell holder and that saves you another 6-8 bucks.
If you should choose to get a three die set (Lee) get the one with the neck sizer, you really won't need the crimper die for those cartridges.
You simply cannot do better for a press than Lee's "Classic Cast" single stage. It is one of the most rigid and precisely made presses on the market and the price is fantastic for the quality.