(Been 3 times so far.) That's not far off. On our last entry, not counting safety gear each person coughed up ~$600.00 and we really should have brought 2 more tires. If the car lasts till season 2, the costs drop dramatically.
You will have to do an entry essay. Don't bother trying to impress them with your Johnny Gearbanger racing resume, they will chunk it in the trash immediately. They aren't looking for racers, they are looking for party people.
First time LeMons racer: forget anything with an automatic tranny. First choice would be an econobox in good running condition with body damage, but there's so damn many of those they tend to bore the LeMons judges. After that, 4 or V6 RWD imports (240SX, 300ZX, '80's Celica, RX7 etc) and bottom of the barrel would be big V8 American cars. I'd personally like to stick a KA24DE in a Fiat 124 spider or similar, that should get the judge's attention. They like weird stuff but the problem is the weirdo cars tend to be fragile. Catch-22.
Do not cut corners on the cage, if you or your teammates don't know how to build a truly safe cage farm it out. I saw two or three cars fail tech at CMP for poorly done cages. There is no fun in trying to procure a welder, tube bender and tubing notcher 12 hours before the flag drops, 'cause you will NOT get your entry fee back if it doesn't pass.
Go for reliability, not speed. Keep the damn thing circulating out there! Drive clean, the less time spent in the pits or getting the oh so funny punishments the better. Handling, braking and reliability counts for more than speed, leave the motor alone (so it'll last) and concentrate on making the car stick to the pavement. There are a ton of inexpensive (many are free!) tricks to make a car handle. Invest in decent brake pads and add brake ducting.
The Falken Azenis works very well, I drove them in an absolute cloudburst on Day 1 and was pleasantly surprised at how well they worked in those conditions. In the dry, they were great for 4 or 5 laps then started getting greasy but not uncontrollably so. I have heard good things about the new Dunlop Star but have no direct experience with it.