Need a recomendation.

I'm gonna say this in list form cause my first post got deleted and it'll be faster.

1. Bought 96 Dodge Neon.
2. On long trips it started to buck.
3. My dad replaced the fuel filter.
4. It, apparently, stopped bucking (haven't driven it on many long trips since).
5. It ends up having bad gas mileage.
6. My dad recommends having the fuel injectors blown out.
7. I sent it to an auto-mechanic and when he gets back to me he says it may just need a tune-up but he could clean the injectors.

What do you think? Blow out the fuel injectors? Clean them? get a tune-up? A combination or something else?

These days a 'tune-up' only amounts to changing the spark plugs, the plug wires, changing the air filter and fuel filter. And hoping that makes it run well again. There really isnt anything you can adjust in terms of ignition timing or fuel mixture.
You could measure the pressure in the fuel rail, but its likely to read 49 psi at an idle, even if the filter was partly clogged. The meaningful measure of fuel pressure would be one taken while you were buzzing down the highway at 60 mph; which involves expensive gear.

So; I would think bad gas mileage might be a dirty or failing Manifold Pressure Sensor, a bad coolant temp sensor, a Throttle Position Sensor problem, an EGR valve that is stuck partly open, even a layer of crud built up behind the throttle valve. Or any of several other things.
If the engine runs on all 4 cylinders most of the time, then I dont think its an injector problem. If one of them is partly clogged, I think it would be a constant issue.

We have a 97 Neon that was bucking a lot, but at least kept running. Its up for new tags in September, and has a slight amount of blue smoke from the tailpipe. We have emissions testing in this area, and it wont pass if they see any smoke from the exhaust. So I think I will have to pull the motor and rebuild it.

Add a new PCV valve to the list of tune-ups. Often overlooked, but when it sticks, it can cause problems. About a $5 part at most stores.

Okay, thanks everyone. Now I've got a newly compiled list:

1. Replace the O2 sensor,
2. Clean the injectors
3. Test the ignition coils,
4. Put in new properly gapped spark plugs
5. Get new spark plug wires
6. Have the timing checked
7. Get the computer scanned for codes.
8. Making sure the car is properly tuned.
9. Check the manifold Pressure Sensor
10. Check the coolant temp sensor
11. Check the throttle Position sensor
12. Make sure the EGR valve is not stuck partly open
13. Check behind the throttle valve.
14. Replace the PCV valve to the list of tune-ups.
15. Make sure the tires have the right pressure
16. Change the fluids
17. Replace ait-filter
18. Check the cam shaft sensor
19. Replace the distributive cap
20. Replace the rotor
21. Wipe down engine
22. Use a lot of seafoam.

Anyone wanna add anything else?

19. Replace the distributive cap
20. Replace the rotor

You can remove these two as the neon does not have them. It uses the coil pack instead.

I hope you will keep a journal of what you do, with the mileage and date, and maybe a note about where you got the parts (in case you need more of them later). I do this for each of my cars. Its very helpful in planning what to maintain or fix next. With an old car, there are going to be things that are failing -for the first time-, that wont be common failure items on younger cars.
Much of the stuff on your list amounts to normal maintenance for an older car.
#15 is one that you should check at least twice a year for instance - and more often if one of your tires loses air faster than the others.

My 95 would buck when coming to a stop after driving for a while. I won't give the list of things that didn't work. But finally changing the throttle position sensor fixed it.

Thanks again for your help.

Can anyone tell me which 1s I can do myself?

Buy a Haynes or Chilton's manual and you can do all of them by yourself.

Buy a Haynes or Chilton's manual and you can do all of them by yourself.

Well, I know I could eventually do all of them myself, but I meant which 1s would be easy and I could do with only a little work and expense. Besides I don't have the equipment to do a lot of stuff, and buying it would end up being more costly than paying a mechanic.