How many bike specific tools do you own? You do understand that the amount of proper tools you need to build a bicycle isn't cheap....just a proper repair stand can cost $100+ Take a bare frame and a box of components to a bike shop can easily exceed your $100 just for labor.

Building a bike from a frame isn't as easy as most people think.

If you want to learn to build/assemble a bike, it's better to start off with something cheap/used to mess around. That way when you screw it up, it's not a huge deal. Plus you can focus on one area at a time and aren't forced to assemble a complete bike at once. It also makes it easier on your wallet to buy the bike specific tools for each area of the bike...instead of buying them all at once.

If you had decent money to play with, I would say go ahead, build the bike. But building a bike on a budget is similar to people that try to start car projects on a budget...it always costs twice as much as intended because trying to save money results in cutting corners/not installing the parts correctly (and at the end, you end up paying a professional $$$ to do finish it/repair your screw-ups).

For $300 you can pick up a Windsor which isn't a bad first bike. There is minor assembly but if you search this forum, you'll find many "new bicycle mechanics" screw that stuff up too.
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