When I showed dogs, we were on a strict **** schedule. Vaccinations protocols have changed, somewhat. Usually the first shot is a DHLPP. The L is the Lepto vaccine which some do and do not give. I recommend giving it. Yes, you have to be get the Parvo and Distemper started. If you are working with a Vet. Get on a puppy plan which is about every 2 -3 weeks thru 4 months of age. By then, the maternal antibodies (assuming the ***** was vaccinated) wear off. Just because your puppy has had one or two shots does not mean it is protected and you need to protect it from possibly contaminated environments ( parks, public places, etc) during this time. Socialization is important so only take it to safe places. You have to make sure your puppy is free of parasites so take a fresh stool sample into the Vet to be check and get meds if needed.
If the Vet is too expensive, check fir shot clinics in your area. Most cities have them now
If they are still feeding, you'll probably have to wait a little bit longer but the process should be started anywhere between 8 - 12 weeks to make sure their mothers immunity has worn off. The most important one is the Distemper/Parvo, [DHPP]. That is a set of 3 every 4 - 6 weeks and then yearly after the last booster. The rabies shot can't be given until 20 weeks I believe. And depending on where you live its either yearly or every 3 years. There is also a Coronavirus and Kennel Cough one, but unless you plan on having your dog stay at a dog hotel while you are away, those usually aren't as important. If money is tight, those can wait.