To begin with any socks will be ok.... You can always buy some running socks later on when you're doing longer runs - ideally sockd that will wick sweat from your feet, dry rapidly and less likely yo cause blisters
It is worth getting the right shoes - a running shop should give you advice and let you try shoes before you buy - unless you have a problem such as severe over pronation (often due to low arch or foot "collapses" in when you run) then a good neutral shoe is an option to start with
If you already have any issues and use insoles/ orthotics then you should use the same in a neutral shoe
A general rule is at least half a size up from what you usually wear.
And shoes should fit and be comfortable straightaway... Any discomfort is bad - don't assume they'll bed in and feel better once worn a bit .....