Congrats on the pup!!! I would go with the medium collar. You don't want one too big or it will slip over his head. Pups are small. Get an inexpensive one to start with since pups grow quickly. Also, don't get one too wide or stiff. A nice comfy collar is best. A 2 quart bowl would be great for water but the one quart size is plenty big for food. Take a look at a 1/2 cup measuring cup and you will see that it's not very big. We feed 1/2 cup at each meal so you don't need a huge food bowl. Corgis, at least our's, drink lots of water so go with the 2 qt one. Change the water at least every day and be sure to wipe out the bowl when you do. Would you like to drink old dog slobber from an unwiped bowl? Yuck, I know I wouldn't!!! He will tell you when he's gone far enough on his walks. Watch him and when he looks like he's getting pooped, go home. Pay attention to the heat and humidity. Rocky is not a heat loving guy but Rosie would go til she dropped. Take some water with you on hot days and something to drink from. I've used those blue poop bags, unused obviously, as a water bowl. Fold down the tops so they can get their heads in pour in water. Works great!! I'd wait until he was a year before taking him running. Let him run all he wants in the yard at his own choosing but running on a leash needs to wait. I give a solid NO to retractable leashes. The trainers at our kennel club say all they do is teach a dog to pull since the dog has to pull to get them to extend. The skinny little things can hurt dogs and people with nasty rope burns and cuts. A 6ft leash is what trainers want and gives you much better control on walks. If you want a longer leash for teaching, get a piece of light rope and put a snap hook on the end of it and use this. Works great, is cheaper, much better!!
I would just buy an inexpensive medium sized collar for now. His neck will probably get quite a bit larger so I doubt you'll get away with using the same collar for long. You don't want it to be all huge and bulky when he's a pup though, get something that fits and is light weight with an easy to use buckle.
We use a smaller bowl for food and a giant bowl for water. I would suggest going to petsmart or petco and just looking at the items you're interested in so you're getting the correct size if you order online.
We used a medium sized kong for puppies, and upgraded to a large later on. They still use both sizes.
I would only do short ~20-30 minute walks with him at this age, and as much free play as he wants. I would not take him running until he was at least a year old.
I personally hate flexi leads. If the dogs suddenly runs to the end of the rope it can snap off and then you have a loose dog. I don't think they are good for teaching loose leash walking either because there is always some tension on the line. I'd just buy a long regular line for working on recalls if you need it.
Classes are almost always once a week unless they specify otherwise.
When I brought Ellie home at 10 weeks old, I had a small-sized collar (11-14") ready for her. It ended up being too big! If possible, have the breeder measure your pup's neck size close to when you'll be getting him. My breeder had measured Ellie at 11", but it turns out she was more around 10". You'd probably be better off planning on getting more than one collar between now and when he's done growing at 2. ;)
I'm not sure about the food bowl sizes, as I bought mine from the local pet store.
For Kongs, you can get either the medium or large, it doesn't really matter. The color is the more important part, as the black is the toughest. Red is the next toughest. For a puppy you'll probably want to stick with red or below.
Regarding exercise, be sure that he is fully vaccinated before you take him out on walks. Since you're getting him at 4-5 months this probably won't be an issue, just be sure that he has all of that vaccinations taken care of. :)
You do not need a retractable leash. Using a retractable vs. non-retractable leash is a personal choice so you can go ahead and use what makes you feel comfortable. :) Personally, I like an ordinary 6 ft. nylon leash.
I believe the Petsmart training is once per week for 6 weeks, but you're free to choose which day to come in based on what days and times they will have a trainer running a class.
I've used adjustable collars for my puppies, they last longer and you can keep them the right size as he grows.
When your puppy is teething this might help..... wet a washcloth, squeeze it out into a sort of rope, freeze it. Let him chew on that when his gums are sore. It'll help alot...at least it did when mine were pups.
Don't push the running part, two of mine like it (only one stays in a relatively straight line, though) and the third one hates it. You pup, when he's old enough, will let you know how far he wants to go, I think. One of mine, too, will walk til she drops, the other two let me know in no uncertain terms when they're done.
You are going to have SOOOOO much fun! I'm jealous.
Finally, and most important....post lots of pictures here so we can see!