Revival Animal Health (www.revivalanimal.com) has all kinds of vaccines for dogs and cats, among other things. You can just call them and tell them that you want the correct needle size for a dog for vaccination and what vaccines you want as well, and they will direct you.
I have done a lot of research regarding vaccinations over the last 25+ years and would suggest spacing them out as well as not giving 3-way or 5-way vaccines. It is completely unnatural for anyone, dog, cat, or human, for that matter, to have the body exposed to everything at once as is found in the 3 or 5-way vaccines. It is asking a lot for the immune system to deal with such an onslaught of antigens, whether they be modified live or dead. Single-antigen vaccines make a lot more sense, given a few weeks apart, and are much more natural. Revival sells those vaccines as well.
As far as giving the actual vaccine, it is quite easy. Just pick up the dog's scruff a bit and give it into the skin there.
I would also recommend reading more about vaccinations, in general, and perhaps following the vaccination protocol recommended by Jeanne Dodds, DVM. She is known and respected all over the country and has done a lot of research regarding vaccinations. Her protocol can be found all over the internet. Here is one such place: https://www.animalhealthfoundation.org/blog/2017/12/dr-jean-dodds-dog-vaccine-protocol/
Either way, doing the vaccines yourself (except for the rabies as others have mentioned, which must be administered by a veterinarian) will save you a heck of a lot of money. The same is true for any type of deworming you decide to do. As far as dewormers for dogs, fenbedazole, sometimes known as Safeguard, is one of the best ones out there, covering a lot of worms, including whip, hook, and tape worms, and even giardia (not a worm, but a single-celled organism). Fenbendazole is also known to be one of the safest.