a character who is morally neutral, straight in the middle
when I think of someone who is completely neutral (neither good or bad and right in the middle), I think of someone who only values his self-interest
I'd suggest first identifying what makes a character morally 'bad' and morally 'good'. You mention self-interest, so let's start there:
morally bad: I am more important than anyone else, so I'll do anything to favour myself, even if it means hurting others (not necessarily physically).
This is the person who'll stab friends and co-workers in order to improve theit life, and who doesn't care at all for anyone else's problems - the only real problems are their own problems.
morally good: of course I am important, but definitely not at the expense of others and, besides, there are situations where my needs take second place in reference to others. Some people have such bad problems in their lives, that I barely have any problems at all in comparison.
This is the 'nice' person who'll always find a way to help out someone, whether it's a friend or a stranger. If they're contending for a promotion, they're very likely to praise their rival even if it can hurt their chances.
morally half-way: I'm important and I'll fight for my chances... but not at the expense of others. I'll also help others in need... but not at my expense.
This is the person who may feel the desire to help out a stranger, but that might cause them problems (eg. arrive late to work) so they carry on and hope someone else will stop to help. They'll do anything to get the promotion, but won't be really able to stab any work colleagues. Unless it's a stranger they don't even know and doesn't really exist in their mind. But it still feels a bit bad.
One can think of other characteristics and see how they change across the moral range. It helps if you can think of actual people who can exemplify the good, the bad, and the half-way.
Once you've done the step above, throw them in a situation and see how they act.
Scenario: Say that the three characters are waiting for the train and someone's briefcase falls down. Tens of paper sheets spread everywhere, wind picking them up and spreading them even farther. The three characters witness the briefcase owner's panic as they try to get the tens of paper sheets.
The bad thinks 'should have been more careful', and forgets the briefcase person.
The good will automatically start getting the paper sheets.
The half-way may hesitate, but will join the efforts.
The train comes in!
The bad goes in, intent on finding a seat.
The good may look at the train, fretting for a moment over missing it and being late... but will remain and help get all those paper sheets. The poor person is obviously in distress and who knows how much this can hurt them professionally! Being thirty minutes late is nothing in comparison.
The half-way will hesitate. They may even want to stay and help out, but we're talking a complete stranger here. Is this person really worth getting in trouble at work? They'll quickly hand in the paper sheets they've collected and board the train. As they watch the stressed briefcase person and another stranger helping them, the half-way will wish they could have stayed and helped. May even wish to be brave enough to do so.
If the bad happens to see the stranger helping the briefcase person despite missing the train, they'll probably scoff at the idiot.
In my experience, most people are flat in the middle of this 'moral' range. Then there are a few who'd sell their own parents if that meant a promotion, and the few who'd cut off a hand to help a friend in need.
Choosing a good story goal
Personally, I'd say to focus on the character and see what they want. What is their aim?
Then decide if you (as the author) want the character to succeed in reaching their aim, or if not reaching it will teach the character something important for their personal growth.
Let's say the MC's aim is to get a promotion, only a work colleague is also trying to get it. Then there's a situation where the MC could kick their rival out of the promotion race... Temptation! Do they have the guts (or are they mean enough) to do it? If so, could they face this colleague they'd never had problems with before?
In this scenario, neither the bad nor the good would hesitate: one with go for it, the other would be outraged at the idea. But the half-way... the half-way will hesitate. Will they do the honourable thing, or will they sell their soul?