Car seems to be coasting when I first start it - won't engage in gear?

It always happens when I first start my car, and sometimes when I start it throughout the day: When I start my 99 Honda Accord LX and give it gas, it doesn't want to drive or reverse, as if it can'g engage. It last a few seconds. My breaks still work during that time, so I have control of the vehicle. It feels like it is coasting until it can engage. I was told by a friend this is likely the transmission going out. I changed the transmission fluid at the Honda dealership and this did not fix the problem. It does not seem to be leaking anywhere that I can tell, and the gauge shows that the fluid level is fine.

I'm wondering what the next thing to test should be? I know transmission fixes are expensive, and I'm planning on getting another car soon. I'm just wondering what kind of time frame I still have with this one?

Once I start it and get it to engage, it drives just fine, and usually on other startups during the day are more graceful. There's a definite rumbling when I start it and sometimes a clunk when I get it into gear. It's an automatic. Sometimes when I give it gas, it seems to stall out and the engine dies, thought all the lights flash on in the car. Restarting it and trying again usually get it to go.

Any advice would be appreciated!

It sounds like you have a major transmission problem from your description. As for the time-frame to get it repaired, I'd get something done now - as in, before you drive it anywhere else. It's possible the car could go on for weeks or months driving just as it drives now… But that might actually be more dangerous than if the thing just suddenly won't move away from a stop at all any more. If the thing randomly decides to not accelerate at a time when you absolutely need it to accelerate for your own safety (say when you're pulling out onto a busy roadway for example) and it stalls out in front of something that can't stop in time to avoid hitting you, the resulting wreck could end up seriously injuring you or worse.

Right before that moment of impact, I assure you that the cost of a transmission repair won't be your first concern so I'd either bite the bullet and get it fixed now or just decide to scrap it if the cost to fix it is too high and get something different that won't potentially endanger your life every time you drive it.

A) It's BRAKES, not breaks.

b) The automatic transmission is taking time to build up pressure after starting. Low fluid can cause that, but so can a failing torque converter which would require the transmission to rebuilt. If the fluid is topped up and clean, which apparently it is, then the transmission is going and you do not have a lot of time before it fails altogether. Get rid of it NOW.

Have you now or in the past checked the fluid level?

This year was in a group of years that had bad torque converters that were shelling out, tearing up the trannies. I had an '01 with the problem. There was an extended warranty up to 60K miles. I got mine in just under that. I think there was a recall. Now you need to decide if want to spend $1,500 or so on a rebuild.

This is my suggestion. DO NOT take it to a place like AAMCO. They are a transmission store, and have a huge markup on parts. Find an automatic transmission shop that is ATRA certified.
http://www.atra.com/shopfinder

Sell the car as-is and get a new or newer car. The cost of repairing the transmission will be more than the car is worth. Pass the car's issues to the next owner.

"Should you find yourself in a chronically leaking boat, energy devoted to changing vessels is likely to be more productive than energy devoted to patching leaks." Warren Buffett (the second richest man on earth)