OK, I've seen this topic come up several times and i didn't find a good comprehensive thread right away so I thought we could put together all the advice and specifics for: 1) a beginner ordering a complete bike from FF to...
2) advanced tools and custom mods that you guys use.
I will get things started with all the basics I've collected over 20 years of riding flat.
ALLEN SET
I use these almost everytime something gets worked on with my bike

My bike uses both the Metric and SAE for different parts so I went ahead and got both.
CRESCENT WRENCH (ADJUSTABLE)
SOCKET FOR YOUR 3/8 or 14mm axle nuts.
DK TOOL WILL GET YOU THIS FAR - a handy tool to have around for a beginner
WIRE CUTTERS
Go ahead and get good ones that will last. Unless you never run brakes.
GOOD HIGH PRESSURE PUMP - $35-40

If you flatland you will probably use this every time you go out. Best $40 I've spent lately.
CHANNEL LOCKS
OK, just looking at this makes me cringe. I try to NEVER use this. If it pick it up I know that I'm going to grind and round off a little bit of some bolt somewhere no matter how careful you are. However, if you have some older parts, an American unsealed BB, or headset nut - sometimes this is just the best thing to use to break it free or get it tight. If you can spring for the right size 36mm wrenches (below) that is better but this will serve multiple purposes in the long run.
LITHIUM GREASE
This is what I use from WalMart - get Lithium. But if you notice everyone on here swears by the PHil Woods Grease.
OILI use this on my cables when I'm too lazy to pull them out and grease them. Do NOT use WD-40.
BIG UGLY HAMMER
Enough said.
TIRE LEVERS
After 40 minutes of trying to get one tire on with my bare hands, I broke down and spent the $3.99.
GREASE RAGS
Just go buy a set of 10 from a local store.
CABLE TIES Again this is more for brakes, but I use them frequently.
CHAIN TOOL
You probably won't use this a ton unless you are switching up sprockets and gears or bikes all the time. I like mine.
SMALL TACKLE BOXKeep everything!
TUBES AND CABLESTwo things I always buy more of everytime I order from FlatlandFuel. It's either $1.99 from Pat or $6 when I need it from my local guy. Seriously the last jam I went to I got a flat in the first 10minutes of being there and I was thankful for the guys that had a spare tube (thanks Danny). I swore to always keep spares. I keep a few extra cables too just in case.

CLEANER
THE BEST!
SPOKE WRENCHDon't even try this unless you learn how to use it. But if you learn it can keep your wheels straight for a lifetime.
TOOK KIT = $60This may be worth it for starting out with nothing.
BIKE STANDI don't personally have one of these but everyone that does swears by them. $70-$120
GOOD WORKSPACE
I would also hope that most local shops or local riders would be cool enough to take the time to stop and really teach you how to dismantle and maintain you bike. It may be worth some time just to come in a shop on a slow day and ask them to show you how they fix things up. Some basics. Or ask a local rider to help you. Sometimes the best way to learn is just to take something apart slowly and put it back together. Chances are high that you will get it right and learn something in the process.