I know what you are going through.
I had to have my baby, Cassie (I fondly referred to her as Mama), put down on January 9 of this year (my Dad's birthday). I used to work as a vet tech, so I had assisted with pet euthanasia before, but this is the first time I ever had to do it for my own pet!
Cassie was my only pet - we were very close and it was that much harder for me. But, when I looked in her eyes, I knew that I did not want her to suffer. Her illness came on quickly, and that made it even worse. But I held onto her and told her I loved her; she closed her eyes and was gone.
I had her cremated because I just couldn't bear to have her put in the cold, winter ground - she soooo hated to be cold (just like me). I placed her remains in front of her favorite window in the den of our house. I miss her, but just having her "with" me has helped me to heal. That and the fact that the vet and the pet crematory were so kind and caring. They treated both her and my family with respect - it was amazing.
That being said, what you don't want to do, and this is my opinion, is rush out and find a new pet. Allow yourself time to grieve the loss of your current pet and to think of the things about your pet that made you happy and whatnot. Then, you'll be able to find out what is best for you.
I know because within days of Cassie being put down, I was on websites looking at animals to adopt. I had to stop (one, because I wasn't allowing myself to deal with the grieving process and two, no other pet could ever replace Cassie - ever).
So, I say, if, God forbid, you have to put her down, take a while, a few weeks or months afterward and just enjoy her memory and give yourself time to grieve her properly.
When it is time for you to welcome another pet, you will know...
Hugs and best wishes to you...
Fantam