The best advice I can give you, which is also something most players will tell you not to do, is to Netdeck. Netdecking means you look up a deck list online and copy it. While making your own deck from scratch and working through all the "learn as you go" phases of Magic is fun, I always find it easier to teach someone how to play when they have a good, solid deck and a chance to actually win a game or two vs. experienced players. Netdecking guarantees that a new player will have a deck that is consistent and well built, letting them learn the game from a standpoint that'll provide solid skills in the future.
I'd go
here and make use of the site's resources to netdeck. TCGPlayer covers all the major tournaments for Magic the Gathering and publishes the deck lists that did the best (usually the top 8-16 players). Note that buying a deck outright can be expensive, so you might want to choose a price limit per card. I'm just getting back into Magic myself after an 18 month break. While I would love to buy a super-powerful deck and just roll people left and right, I don't have $400-600.00 to spend. I do, however, have $100-200.00, and am willing to pay up to $15.00 per card. Since most cards will fall somewhere between >$1.00 and $5.00, this works well for me and I've already bought a pretty solid Black/Blue Zombie deck with that kind of budgeting in mind. Since TCGPlayer features multiple decks of the same deck type, you can sort of see what's absolutely necessary for that deck type and try to cut costs accordingly. Keep in mind that some decks are so popular and/or use cards that are widely used that you might not be able to buy that type of deck with your set budget.
You'll also want to buy some starter decks and booster packs. You mentioned that you enjoy Blue, White, and Red. Buy the Starters for those colors along with some packs of the most recent set (Dark Ascension). This will give you a small collection of stuff to work with and possibly some trading fodder to get other stuff you want.
When it comes to trading, trade cards based on their market value. It's the easiest way to ensure you aren't getting ripped off as a new player. I personally use TCGPlayer's average price to gauge what a card's worth is, since TCGPlayer bases their card prices on the prices found at multiple online stores. For example, let's say someone has that Liliana of the Veil I've been looking for. Liliana of the Veil is worth $29.55 on average, according to TCGPlayer. If someone wanted a Havengul Lich ($13.09), and two Gravecrawler ($7.92) from me, they'd want $28.93 worth of cards from me. Going strictly off of price, the trade is about equal.
It's ALWAYS easier to buy the card/s you want individually instead of buying packs and hoping for the best. Buy packs to increase your overall collection and to get things you can trade with other players, not as a direct source for building a deck.
If you want to enter a tournament but don't feel like your deck is up to par, try the Booster Draft tournaments. It's a good way to get cards and build up your deck building skills.