Mums Funeral and New Boyfriend?

my mum was a long fighter of cancer, and unfortunately passed away on 14th Feb, however, in October i started a new job and there was a guy there called Sam, my mum saw straight away that we hit it off and would constantly ask about him, and tell me to get to know him etc. one month later we begin dating, she's really happy for me. but she's getting ill by this point, so just before xmas he came over for a day and they met. she liked him a lot. my dad likes him too, and they've met about 3 times now (we don't get to see eachother often outside of work) anyway, mums funeral is in 2 weeks or so, i've met Sams dad twice but never his mum, however she sent flowers and a sympathy card. Sams dad had met my mum but his mum hadn't. they've also invited me out for a meal next saturday - i can get quite nervous and awkward around people i don't know - so what do i do and how do i prepare??!! also should i invite Sam and his parents to the funeral even though they barely met my mum?? i don't know what to do!! please note that the funeral is for mums friends and we are having a wake and separate private burial just for family and close friends, but do i invite him? my best friend will be there.. thank you xx