Totally, you just have to be aware that without the MM you won't be fighting monsters. without monsters the only other combat possible is PC vs PC combat, which is not what the whole combat system was designed around and is actually discouraged.
I would heavily recommend getting the MM2 in order to get a solid grasp as to what is considered balanced and fair from level to level. There is nothing to say you couldn't run a game without it, but it is very much worth the investment. I say MM2 because the monsters there are better tweaked than in MM1 given the additional playtesting. I'm sure the same will be true for MM3 when it eventually hits the shelves. Using the 'monster' tables you could then have a great template for your arsenal of human encounters.
The DMG on the other hand is really unnecessary. It contains a good bit of useful information, but nothing that is truly vital to the game.
The one book missing from your list that I'd also highly recommend is the Adventurer's Vault 1. While not essential, the PHB1 really lacks in equipment options. If you intend to run magic campaigns, then the AV1 is a great addition and will prevent houseruled items that unintentionally break the game.
I'd very much recommend mini's in the game as D&D 4e gears towards those elements of combat more than prior editions. The combat is more tactical than prior editions, and this element could easily be lost or weakened without mini's or a grid. Of course mini's are easy to get. Just use chess pieces or marked poker chips/change if you're trying to keep your expenses as low as possible.
I'm wondering about a campaign in which:
about 70% of those the PCs fight against are humans
about 30% of those the PCs fight against are unique monsters created by the DM
Could a DM with nothing more than the PHB, dice, and pen and paper accomplish that?
Why does the system discourage the PCs from fighting NPCs? How would this be sub-optimal?

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.