My condolences on your loss OP. I think you are dealing with several issues at once and it might help you to pick them apart a bit to work out what to do.
First of all, you have the issue of what to do with your mums remains, I am assuming there is no family burial plot and that she didn’t leave instructions for a burial, therefore you are looking at a cremation. In some ways this could make choices easier, as if you felt you couldn’t make decisions at the moment you can ask a funeral director to arrange for a simple cremation without any service then ask them to keep your mums ashes safe for you until you have decided what to do next.
You then need to think about how you do want to celebrate your mums life and give people, you included, a time to recognise her life and mourn her passing together. This does not have to be a formal service, though it can be if you want it to be, in which case you can speak to a priest or vicar, or a celebrant, and arrange where you want the service to be, (not necessarily a church, chapel or similar but could well be), who will speak, what music or songs/ hymns will be played etc. Your mum can be represented by an order of service, photos, or her ashes, or flowers, it is up to you. Or it could just as easily be an afternoon tea , in a hall, or a back room in a cafe or pub, or at home, when friends and family can come together and remember your mum, listen to music, or a reading, or a poem, or just chat. One thing to remember is that there is no rush, you can wait until you are ready.
Which is the third thing , your well being. You are probably feeling overwhelmed by all the paperwork, decisions, working out what to do with her personal effects etc, and at the same time you are dealing with your own emotions and early grief. So be kind to yourself, and allow yourself to recognise the hard steps you are taking, to remember your mum in your own way, and take pride in the way you are dealing with her death and your grief, while at the same time honouring her memory.
Be kind to yourself.