I used to play magic in 90's, but since that I've only played a few random games with my friends' decks. This post gives you a view to the game from a magic player after getting back to the game after a long, long time. While the new rules felt intimidating to me first, they actually make perfect sense and are much simpler. I'll also write a bit about what you should know if you get back after a long break and what should you be getting. I say straight away that currently random packaging puts me completely off, so I'm getting my cards in non-random packs or as singles.
What should you know if you're getting back to MTG after a long break
First, if you're curious about magic today, you might want to check out the new rules. The biggest changes are that Interrupts are gone, there's just instants (and mana sources that just give mana). Instants go to stack, where top events of the stack are checked first, and there's no interrupts to confuse this, which is good. Removing the source of the effect still doesn't cancel the effect. Artifacts function while tapped, and power level is completely different from the days I used to collect (4th edition, Ice Age, Homelands, Alliances etc).
Creatures are generally much stronger than they used to be. Many of them do more than just hit, possibly when you bring them to table, or gather easily handfuls of tokens. There are new core mechanics that are extremely powerful you should know about: Double strike gives the creature a first strike attack in addition to normal one, Proliferate lets you increase amount of counters on your cards, Infect gives -1/-1 counters to creatures they damage instead of damage and act as Venom against players, so 10 will eliminate a player.
(A note about the photo on the right: These cards have nothing to do with the ready Commander decks - except the decks got me into the game again and buying some new cards!)
It isn't the standard (or legacy) format that got me back in the game. My friends had been playing Commander (or EDH, Elder Dragon Highlander) and got me in one game when we couldn't get a rpg session up. In Commander, you play with a 100-card highlander deck, so there's no two same cards except basic lands. Btw, I just got it even if I had using the term for ages - 'There can be only one'. Heh.
In Commander format, you choose to get a commander, a legendary character that is outside the deck and can be cast from the command zone, and may return there (with increased cost) if killed. The rest of the deck can't have cards with mana symbols that the commander doesn't have.
I had to face it that majority of my cards didn't have anything to do in current games. In addition to having lots of doubles or sets of 4, many of my cards were completely outdated. Lands of course are usable and some separate cases, but then again, spells like Lightning bolt that are excellent otherwise aren't that good in Commander, so there was quite a little I could use in the current gaming. And Balance, which would have been excellent, is forbidden. Maybe for a reason.
Like I mentioned, I don't want to get into randomized boosters anymore, and also I'm on a budget. What I'm suggesting is that you choose and buy one or two of the new Commander decks, which help you get in the format, gives you some image of how powerful cards should be and how the commander decks should be built. And each of the decks has for example Lightning greaves, Command tower and Sol Ring, which are quite essential in the game, in addition to getting a few very strong commanders. The other cards are hand-picked too, so they work well as a deck and are mostly quite good in general too.
And speaking of Prebuilt decks, some collectors may disdain them, but I can tell that they mostly have a good amount good cards, which help you get a good card base. I bought Ajani vs. Nicol Bolas duel decks and am quite happy about it. The disdaining collectors have gathered the same cards by buying display cases and may have multiples of each common or uncommon, so I understand the decks have little value for them.
Gatherer (link at the bottom) is a magnificent tool you can use to find the cards you'll want. If you're using Advanced search, you can search the things you want and choose to display all that have 3.3 or more as their community rating, or if you're on budget search for 4.5 or better and just commons and uncommons. This has a disadvantage though, as some cards become good in multiplayer games, and some are not so good in multiplayer.
Official MTG rules
If you're interested in Commander format, here you'll get basic information: http://mtgcommander.net/rules.php
If you really want to get in the format, read this: http://forums.mtgsalvation.com/showthread.php?t=291478
Gatherer: Your tool to find your cards: http://gatherer.wizards.com