When I start from a stop it'll occasionally miss. As i accelerate itll eventually go into 2nd or 3rd gear but it seems late in doing it.
Am I looking at a big-$$$ bill to fix?

Well . . . it'* difficult to diagnose based on what I know so far. A complete overhaul for a 4T40-E is around $1,800.00 in my area, however, the behavior you've described so far could be caused by a number of things that don't require major work. "Could" but no guarantee especially at 200,000 miles.

How many miles since the last transmission service?

Have you checked the transmission fluid level?

How many miles since the spark plugs have been replaced?

How many miles since the spark plug wires have been replaced?

Is the check engine light on?

How long have you owned this car?

How many miles have you owned this car?

Does this happen more often when the engine/transmission are cold or warmed up or doesn't matter?

What part of the world does the car live in?

What do you know about the car'* history? Like: Has it been a taxi cab all its life? Was it owned by a little old lady who bought it new and kept it garaged and it never saw weather and you bought it a week ago? . . . or . . . ?