Different things, so you need to look at different things.
Childminder: Assuming you are in England, the childminder will be registered with Ofsted and will have on display or be able to show you their registration certificate. Ofsted will have carried out suitability checks on the childminder and CRB/DBS checks will have been done on anyone else in the house aged 16+. Visit them and ask about things like travel to/from school, who supplies carseat if travel is by car, ask if you can speak with any existing clients. Tell them you are nervous about leaving your child, let them make you at ease.
Babysitter: find someone local who you and your child get along with. They may or may not have a CRB/DBS check from previous/current childcare work they do during the day. Ask for references, they may have written ones and people you can call. Talk to at least one other family for whom they have done babysitting or whomever they are providing as a reference (it may be their first time babysitting, so they may be providing a character reference from say a youth group leader, or something like that).
With all childcare, trust your instincts. You will know when you meet someone who genuinely likes children.