Welcome
Most start with extract.
A very few start with AG, but they usually have a buddy who can help them through the first sessions.
It's your choice.
All that said:
1) The monetary cost of getting started with enough equipment to brew extract batches is less (though you CAN spend just as much).
2) Even with extract, you need to conquer sanitation, hop additions, water treatment, temperature control, aeration, the boil, dealing with hot break, how to take measurements, how to achieve carbonation, how to chill to pitching temps, siphoning, etc. That's a lot to deal with and get used to doing correctly. That's plenty to worry about on its own.
3) Throwing in AG adds a whole series of issues that make it more complicated, and that's even if everything goes exactly as desired. Throw in problems like how to clear a stuck mash, how to dial in your mash temp, how to tell when conversion has actually occurred and what to do if it didn't, etc, and you may not be in for a very enjoyable first brew day.
I reccommend you try a couple of extract w/grains batches first (using unhopped extract, steeping some specialty malts, and adding your own hops to the boil) just to get the process down. Then once that's easy for you, make the jump to AG.
Use a simple but proven recipe from a known source, in a style that you like to drink on its own.
American Pale Ale is a good first choice. It's pretty simple, uses a forgiving yeast, has a lot of room to cover minor flaws, and even your bud swilling buddies might be willing to try some.
Here's a basic tried and true Sierra Nevada Pale Ale like recipe:
6 lbs pale dry malt extract
3/4 lb crystal 40L
1 oz Perle @ 60 mins
1 oz Centennial @ 15 mins
1 oz Chinook @ 5 mins
1 oz Cascade @ 2 mins
1 tsp Irish moss @15
US 05
3/4 oz corn sugar for priming
Bring 2 gallons of water up to 150 F (measure it with a thermometer).
Steep the crystal malt in it in a grain bag for 45 mins.
take out the grain bag, top up to 6.5 gallons
bring it up to a slow rolling boil. You don't need wort flying out the top. Enough movement on top to keep things moving is enough. Turn the heat off and add your extract, stirring it in thoroughly. Turn the heat back on.
Wait for hot break (the wort will build a big foam on top, then the foam will cave in on itself. This is called hot break).
Don't let it boil over.
At hot break, add the Perle hop addition and start your timer for a 60 minute total boil.
Wait 45 mins until there are 15 mins left on the timer. Add the irish moss and Centennial, and put your immersion wort chiller in.
Wait 10 mins until there are 5 mins left on the timer. Add the Chinook.
Wait 3 more mins until there are 2 mins left on the timer. Add the Cascade.
When the timer runs out, turn off the burner. You should have 5.5 gallons of wort at this point
Turn the water on in your wort chiller to cool it down.
Cool it down to 65F.
Siphon 5 gallons into your fully sanitized fermenter using a fully sanitized siphon, leaving the majority of the break material behind. Getting some of it in there is ok. Just don't dump all of it in. You want to leave most of it behind in the boil kettle.
Aerate the wort fully. 90 seconds of pure O2 is best, though you can hit it with an aquarium pump for a half hour or shake the fuck out of it until your arm gets tired.
Pitch your rehydrated yeast. Attach the sanitized airlock filled with cheap vodka.
Keep it at 67F for fermentation.
Optionally add another oz of Cascade after the krausen falls. Let it sit that way for another week.
Boil a pint of plain water. Add the corn sugar to sanitize it.
Sanitize your bottling bucket and put the sugar solution in it.
siphon your fermented beer into the bottling bucket. Siphon flow should be enough to swirl the sugar solution around and get it all mixed without you needing to stir it, (which can introduce oxygen which stales the beer).
Sanitize your bottles and bottle caps (you'll need about 50 clean and sanitized 12 oz bottles for a 5 gallon batch).
Siphon the beer into the bottles with a bottling wand. Cap and then put all the capped beers into a couple case boxes and store them around 70F for 2 to 3 weeks to carbonate. Don't store them on the concrete floor, as it will suck the heat our and the yeast won't carbonate them.
You can refrigerate them after about 2 weeks or so and enjoy them once they are cold.
There will be yeast on the bottom of each bottle that you'll want to leave behind. Use a glass and don't shake the bottles before pouring.
If you have any questions, ask.
Also check out John Palmer's web site:
http://www.howtobrew.comIt will answer a lot of your questions.
HTH & Good luck!