Most cases, run missions for factions and make some cash.

There are no special missions after the SP game, so just do anything you want. Fly a mission for a faction, hunt for wrecks, trade merchandise or mine. Your level will go up eventually.

Once you finish the story line, how you level up depends on the amount of
credits you make. All the way up to max lvl 38.

Ohh ok so it dont give what amount you have to reach anymore after story end.

Click on your player and it will tell you what level you are. I think it also tells you what you need for the next level. I'll have to load FL when I get off line and check.

As already stated, Level 38 is the highest in SP. But you can go higher in some multiplayer versions.

It will let you know how much you need to make to level up. When you reach that level, the games gives you an audible "bells & whistles" kind of sound like you've heard before.
Now, although in SP the max level is 38, it doesn't stop you from continuing on with your exploring and making credits. I think in the basic SP game, the max credits you can possibly make before something happens is 999,999,999 credits.
I've heard some stories about crashing or character corruption when you make over a billion. But, I've never gotten that far myself to find out.

No it is not telling me what i need for next lvl it just says mission.

Sounds like you're referring to the Nural Net Log??
On your HUD in the upper right corner is the icon in the shape of a man.
When you click on that, a window will open up that shows you what your current level is as well as your reputation with the factions you've already encountered.
Somewhere along the right side of that it shows your mission status, current amount of credits and net worth. It should also show you how much you have to make to hit the next level.
BUT...if I'm wrong on this..and as you say all you see is what you just posted..
There is a set amount you have to earn to reach the next level that's annotated in the ptough.ini file.

Jeeesh....has it been THAT long since I've played it? I lost count of how many times I've played the story line. But I've been busy working on a major mod...
so it seems my memory has gotten a little rusty.

Sometimes when you play SP, it'll say the next level requirement is mission when there aren't any missions. Simply make some cash by doing a mission from the Job Board, selling loot or equipment, and it'll say how far to the next level again.

There are some things that nanobots can't repair. For everything else, there's Mastercard!

I had this problem when I used the OpenSP files on a mod that wasn't specifically OpenSP compatable. No matter how much credits I made it still said that I needed to do a mission to reach the next level. (Though there was no way for that)

Don't know if this is your problem, but hey.