DOTP is a great way to learn. If you're only learning via physical play with real people then you might not learn things like "the stack" or turn order properly. Magic has a lot of little details and rulings so it's easy to get mixed up, but DOTP does a good job of getting you into the swing of things.
One of the biggest things it
doesn't do well, in terms of teaching newer players, is how to build a deck. That part gets a bit more complicated, so I understand that it's not a huge part of the game. Sure, you can edit the decks they give you and to some extent that gives you a slight idea as to how you should be balancing your deck, but it won't really help you when you get out into the real world and start from scratch.
So when you do get around to wanting to build your own deck, either from scratch or heavily modifying a pre-constructed deck, if you need any help at all just let us know! Many of us in here will be pretty quick to help you out, and everyone gives some great advice.
Some basic rules of thumb when building a deck to just keep in mind:
1. 60 cards is the minimum, but you also shouldn't go higher than that. You might hear people talk about "their 75", and they're talking about their 60 card deck and a 15 card sideboard. A sideboard consists of cards that you'll add into your deck (while subtracting an equal amount, generally, of other cards from your mainboard. Your mainboard is your standard 60) for very specific situations. Say you end up playing against a deck that is giving you troubles with artifacts: in that instance, if you have artifact "hate" in your sideboard then you'll want to "side" those in for the next match.
2. Keep an eye on the mana costs of each card you put into your deck. You might hear people talking about their "curve". Your mana curve is, essentially, the rise and fall of mana costs of all the cards in your deck from lowest to highest. If you have a good curve, generally picture a line graph that steadily rises. You don't want too many cards of the same mana cost, because then your curve gets sloppy and you'll likely notice that your progress throughout each turn is inconsistent. For example, if you have too many 3cmc (cmc=converted mana cost, which is the total mana cost for a card. A card that costs 2 mana and one Mountain, so 2R, would have a cmc of 3) costing cards in your deck, then you may find yourself not being able to play anything until turn 3 because you lowered your chances of hitting any of your 1 or 2 cmc cards. Striking a good balance is generally key. However, this can fluctuate depending on what it is that you are wanting to do. You don't always need a steady mana curve, but you should usually strive for balance.
3. Don't skimp out on the land! I think a typical thing that new players do is they tend to subtract lands from their 60 in order to fit in more of the cool spells they like. While some push and pull is okay, it's usually not a good idea at all to remove lands for other cards. In a 60 card deck, you can have any variance of lands that you desire within a specific range dependent upon your deck's objective and mana curve. Typically you'll want at least 20 lands in your deck, personally I almost always tend to run at least 22. But mana curve comes into play here, as well. If you have a surplus of pricey cmc creatures, obviously you'll want more lands in the deck. Here are some examples: In a red goblin deck, you can get away with less lands because your mana curve is very low, which means that all of the cards in your deck are very inexpensive. The highest costing card in this deck might be 3, so you can get away with 18-19 lands. My G/W Aggro Humans deck has 23 lands in it, with the highest costing creature hitting 5 cmc. My R/G Big Smashy Monster deck has 24 lands in it, with the highest costing creature at 8cmc (I also have methods of "fetching" lands from my deck, like Rampant Growth and Solemn Simulacrum). It really just depends on the kind of deck you want to play, looking at your mana curve, and then testing to see how many lands suit your needs.
4. If you are running a deck with multiple colors, make sure that your mana base (as in your total set of land cards and what mana they produce) is correct. If you are playing Red and Green, but you have a lot more green cards than red cards in the 60, then obviously you'll want more Forests/green producing lands than you'll want Mountains/red producing lands. "Dual lands" help with this endeavor, as they count for 1 of 2 colors of mana for any 1 time you tap them. Rootbound Crag is the R/G one, for instance.
5. There is no magic ratio for how man creatures to spells you should have in your deck. That is up to you! When I first learned, I was taught the 20:20:20 rule. That is, 20 land - 20 creatures - 20 spells. I strongly recommend
against that rule of thumb. That locks you into a very set way of doing things, and again I personally like to run more than 20 lands anyway. Me, I'm a creature guy. I like to run decks where the focus is smashing face with creatures. So I tend to have more creatures than spells in my decks. My G/W Human deck has something like 27 creatures and maybe 9 or so other spells, for instance. It works for me. It depends on what works for you, and experience and testing will decide that for you.
My tip for beginning deckbuilding:
Find a card, or a handful of cards, that you really like. Then find synergistic ways of using them together, or with other cards. Find a theme you like, and build around it.
This is a great website for researching different magic cards. You can filter your results to suit your needs, based on standard legality or set/block (scars of mirrodin block, innistrad block, M12 and soon M13 are standard legal right now) and also color.
Deckbuilding is REALLY rewarding, and is my favorite part of the game. Don't stress if it isn't the way you want it at first, either. All decks need to go through testing. You will be having to cut cards for sure, and add others you find along the way. Just have fun with it!