Hmm... if you were talking about show grooming or stuff like that, my answer would be way different.
Even so, I think most of your grooming supplies except for 1-2 things can come from your regular petstore.
Petstore type stuff -
Nail trimmers - Millers forge is considered the best because they stay sharp pretty long. However, you can go to the petstore and pick up a good pair of clippers on the spot. Prefer actual scissor type clippers vs guillotine, just because I think the guillotine blade doesn't stay sharp as long. My personal feeling.
*when you are clipping, don't go for big chunks of nail. You are nipping the ends and looking at the bottom of the nail to make sure you aren't cutting too much off. Most dogs are going to have black nails, so you can't go by the side of the nail. Looking at the bottom of the nail, you should be able to tell when you are close to the quik and need to stop. But nip the ends and don't try to do too much in one clip.
Combs - you can buy a basic greyhound type comb (fine to course teeth). No reason to get too fussy.
Slicker Brush - any basic slicker from the petstore is fine. I'd get a bigger kind. This is my primary brush for everything. I don't really use pin brushes for everyday brushing.
Pin brush - you can get from the petstore. No fuss. You can also get slightly nicer brushes from Sally's or Ulta. Ulta has some wood pin brushes that I kinda like. They won't be as expensive some brand name dog show grooming brushes.
Straight edge shears (for trimming feet) - Conair has nice shears that stay sharp a long time. The yellow handle shears. Trimming feet involves knowing where to cut and how much is too much. You don't need super expensive shears for feet for regular grooming. If you were showing, I'd invest in super pointy nose shears because there's detail work in getting around the toes, but most people don't need that.
Online Orders -
Go on Amazon to look for deals...
Grooming table - believe me it is a big deal for having a dog used to standing still while you quickly zip around and trim feet, blow dry, etc. Having a 24" table at least is a good idea. *I would not do nails on a table, only because it does make some dogs anxious and you want the table to be a happy place.
Dryer - A brand like B-Air is fine. The more you spend, the better the quality. But having a way to quickly blow dry your dog is a must. Especially if you have to keep your dog clean for hospital visits or whatever you are doing.
Thinning shears - I absolutely would make a point of ordering thinning shears online. Plan on spending at least $120 on a good pair. 44-46 teeth.
Mars Stripper - if your dog grows a lot of coat around the neck. You will not ever use a stripper on your dog's jacket. It's primarily for keeping your dog cleaned up around the ears and down the chest.
Clippers (optional - but helpful) - If your dog has very hairy feet (not the top of the feet, look at the underside of the feet where the tufts of fur come out from between the pads) + has hair ears, having clippers is very helpful.
You can have your vet show you how to clean out the ears with clippers. You want to keep the ear hole clear of too much hair to prevent ear infections. You don't want too much hair going down the ear canal.
That's it.