stalling and jumping rpms

[lvtoyotaavalon]

this is my first post, i hope i am in the right spot?
bought a 1997 Avalon a few weeks ago and it just started having 2 problems, (at the same time)

1. when shifting from park to reverse, it stalls. doesnt matter weather its warmed up or not

2. when cruising and i let off the accelerator, the rpms drop, but then jump up and down (+/- 500rpm) before settling

-i cleaned the air intake, air filter, throttle body and MAF with appropriate cleaners. no change
-i plan to change the fuel filter, if that doesn't work;
-i plan to change fuel pump, (should i have fuel pressure tested before i replace the fuel pump?)if that doesnt work,
-maybe its the Idle Air Control Valve?
-maybe its the Map Sensor?
Any help will be GREATLY appreciated! thanks

[fourwheeler]

I can definitely suggest you get the fuel pump pressure read before replacing the pump. Just had to do this on my wife's Ford van, it was out of spec and was causing hard starting.

I would also suggest instead of throwing money at the problem, spend the $50 and have a mechanic diagnose the problem which you can fix yourself. If you buy just one wrong part you have saved the money by having the problem diagnosed. Box of doughnuts can go a long way as well.

Please let us know what the problem was. Best of luck to you and happy holidays.