Using this stuff daily, I can offer you some advice:
If you can do as said above, and pick up some good name brand stuff slightly used but in good shape, do it.
If you are going to buy equipment to work with, then be sure to buy quality. Nothing is more frustrating than trying to learn on inferior equipment, or trying to fix something parts and service aren't available for.
If you can do it financially, buy a bit more than you think you'll need. As your skills improve, you'll be glad you sprung for the right tools.
Harbor Freight is OK if you know what you're buying. I wouldn't buy anything that requires consumable parts, or major electrical items. You'll be SOL in a short order and the store won't be able to help you.
Also factor in some decent manuals, books, or even some education time for what you intend to do. It will go further than anything else.
"Free advice is worth what you pay for it."™