Engine revving, but car moving slowly until higher gears

You could have a shop check pump pressure - usually the cause is a weak pump or problems with the valve body.
Chances are if you just sit in drive at idle, it will also move on its own in a couple of minutes once the fluid warms up.
I never recommend changing fluid after 100k.

sounds to me like you need to get your auto transmission serviced

I sounds like you may be low on transmission fluid. Its hard to say with the limited information yuo have given. If you put it into drive and the vehicle sits there and you give it gas and the engine revs up and then slowly starts moving, it is a transmission problem. If it is low you may have already done irreversible damage. The problem will get worse very quickly. Check your trans fluid immediately.

First- lets change engine coolant sensor/ECT/ and you will be very surprised.Black head with four pins.Be very carefull when change it because there is pressure into coolant system.First-open slowly the cap of engine coolant tank.Then tighten again to safe coolant.Unplug the sensor,remove the pin and pull out the sensor.If the "O"ring/old one/ is still inside-take it out.

This car won't start unless the gear is in the P position. Some times the sensor that tells the computer that the gear is in the P position doesn't make a good contact and the car won't start. Move the gear backwards and forwards until it makes a good contact and the car will start again.

Increased vibration from a vehicle indicates worn out engine supports. This vibration often disappears when revving the engine high, but is very noticeable at low revs.

You can have these inspected and possibly replaced to reduce the vibration cominf from your engine.

Hope this helps.

your post is 1 year old. i started helping others 1 week ago. as a fellow rio owner im here to help there are currentl over 5000 un answered posts. if you still need help re-post your problems .its free to get your check engine light checked at most auto parts stores . write down the codes and meanings. 03 kia rio's are blue booked at about $500.
if you re-post with a code you can get faster help. if your car dont have a code . its hunt and guess . my guess would be throtle position sensor,knock sensor or mass air flow

Sounds like your idle speed is way too high, should be somewhere around 800-1200 rpms. I would check for vacuum leaks.

check the transmission fluid for starters. sounds like it is low. Is tranny still under warranty? I would take it back to whoever did work