I got my dog from a registered breeder and they had a socialisation plan. She came to me with a huge head start. It's a condition of registration and a fantastic policy. At 13 weeks the pup will be much more secure and hopefully will avoid separation anxiety.
I kept the pup in the kitchen unless supervised until fully house trained as I didn't want her trapped in a crate if she needed the loo. She's crate trained for the odd occasion we need it eg when a scared child is over rather than a regular thing
You need a bed, lead, harness, brushes, chewy things suitable for puppies, wee/poo cleaner, water and food bowls (continue to feed whatever the breeder does and gradually transition to what you want), register with bets for flea pills/vaccinations etc. I use a groomer to cut my dog's hair when it gets a bit long.
When puppies are uncontrollable they tend to be tired. It'll be a while before they can cope with full days out. They need lots of naps and short bursts of activity and training. Sniffing is really important so make time on a walk for them to do this.
Read some books and join puppy training so you can teach them what you need them to know. I used a positive training trainer that was all about reward. We got through a lot of dog pate which is an excellent training treat and can replace a meal.
It's a marathon not a sprint with a dog. Yes, the first bit is important but they develop all the time and you have a lifetime to tweak things where you need to. All is not lost with a 13week old puppy. They're a baby still