Everything Virama said, except no, you don't need access to all of the decks immediately. There's enough variety that you are able to beat any deck with most of the decks available -- some opponents may prove much harder than others with a particular deck, in which case, yes, you should switch.

I'll give you a similar example to your case, where I fought the last opponent (Vampire deck) about 10 times and lost. It's an extremely well-built deck that pretty much strangles at every turn you while he goes about his business. But then I tried the white deck with no cards unlocked and did better than I did with my green or white/blue decks with all cards unlocked. I then proceeded to fully unlock the white deck and toasted him the first try.

Think of it as any RPG -- using the same tactics, spells, etc. on every opponent will see you lose frequently. You have to know what works -- that's what the entire game is about.

If you find one deck particularly effective against an opponent (white deck is great against tri-color decks because it's so fast and theirs is so slow in comparison -- even better if they don't have flying creatures), I recommend playing against them over and over until you unlock the full deck -- that will make the game significantly easier.

As you unlock decks, I recommend removing the non-essential cards, particularly if they don't suit your play style and strategy. This will also reduce the amount of lands, so you have significantly fewer total cards, which means you're more likely to draw a rare.