As the title says I’m considering giving 4e a shot, I got MM1, DMG and the players guide for cheap and if possible I would like to stick to those books. I have previous DM’ing experience and I usually like to homebrew stuff but for this campaign I would like to keep things by the books. With that in mind…
Good luck!

Normally I suggest people start with the Essentials line, but the PHB, DMG, MM1 trio can work fine too. Bear in mind there is a lot of errata that you'll want to download from the WotC website, e.g. many wizard encounter spells now have effects on a miss.
http://www.wizards.com/dnd/Article.aspx?x=dnd/updatesarchive
Does 4e lend itself combat heavy dungeoncrawls and that it entails? (Resource management, exploration, combat etc…)
Originally I would have said "No" emphatically because 4e combats easily take an hour to run. However, after running Dragon Mountain for 4e, experimenting with exploration-based skill challenges, and introducing fatigue house rules, I now can say "Yes, with a bit of work."
This is a huge topic, however, so if you want to get into the details I am happy to. It's just easy to get overwhelmed with advice when you're starting a new game system, so I prefer to err on the side of brevity at first.
I hear that the MM1 is badly balanced, is there a good way to save it?
Double static damage modifiers
Reduce elite/solo defenses by 2
Reduce paragon and epic elite/solo HP by ~25%
Give solos a way to shake off conditions
Those are rough changes to bring the MM1 monsters more in line with the math of the MM3 and later monsters. However, there were other design changes that are more complex than crunching numbers, for example the stun-spamming dracolich was overhauled because stun sucks as a condition since it takes players out of the action.
Are there any ready to print power cards that are legal?
Not that I know of. As a word of caution, power cards can enforce "power think" in players and contribute to them forgetting that D&D is at its core a game of improvisation and cool ideas, not a card game with a fixed suite of powers. See the DMG page 42.
Is player option-overload a problem?
Yes, it can be. Since you're limiting your game to PHB1 it shouldn't be as big of a deal for your group.
That said, options overload and condition tracking can be overwhelming for some players; in my group I've noticed the more casual players constantly forgetting modifiers so I've implemented a "if you forgot it, then no do overs" table rule. Also, we use Aiea Tools to mark conditions and pipe cleaners for zones and such.
Anything else to keep in mind?
Do yourself a favor and download a copy of my 4e DM Cheat Sheet:
http://www.enworld.org/forum/attachment.php?attachmentid=52844&d=1348785043
In terms of skill challenges...well they are wonky in the RAW, and there are other homebrewed systems (such as Obsidian here on ENWorld) that deal eith some of the shortcomings. Check out the DMG errata on skill challenges first, particularly the revised DCs. Then, if you can get a hold of a copy, check out Star Wars Saga Edition's "Galaxies of Intrigue" which has a
vastly superior treatment of skill challenges than even DMG2.
Oh, and compared to previous D&D editions, 4e fights take up more space, so assuming you are using a battlemap, plan on it being at least 10"x16", and try to avoid regularly using the 5' wide passages of older editions. Also, 4e fights are meant to emphasize the terrain more, so instead of empty square dungeon rooms, think of the Mines of Moria scene from LotR and other similar "set piece" battles.