Being on government benefits has absolutely no effect on your score.
Your employment or lack of it will display on your credit report (if you report to any creditor that you re unemployed).
What affects credit scores the much outstanding loans you have.
The more debt - the worse it is.
If you have a credit card - pay it in full and watch the score skyrocket.
Not directly but the fact that you are on those programs shows low-to-no income, no real assets (a car is not a true asset), and low chance of having a decent amount of wealth. Credit scores are built by taking out loans and paying them back in full and on time. A mortgage is a huge boost for a credit score, as is the length you've owned credit cards in good standing. If you are on welfare and in a public housing unit you have a very low chance of getting a good credit card (because you are low income) and not having a good credit card can not increase your score.
The general rule is that those don't hurt you but they won't help you at all, either.