I am looking into getting a decent shave kit for around $300. Help me please.

Hello everyone. From my reading, I have seen many knowledgeable members and I am in need of guidance. I'm not sure how to do this so advice is welcomed. My endeavor into this awesome hobby of straight razor shaving was kickstarted by the discovery of my great granddaddies keen edge razor and worn out brush. The razor is heavily used, to the point that it has lost (I'm assuming due to spine wear) 1/8-1/4" of blade, and I need a strop.
Long story short, I would appreciate a shopping list of supplies. Please include brands, models, and where to buy it. My budget is $350. Thank you to everybody 😅

Oh ,man! Are you going to have fun. That's a nice budget to jump in with. I'm newish to this, so I'll let more experienced folks do the heavy duty sherpa work. But before anyone else asks, post a couple photos of your heirloom gear. It's the best loved stuff, if it came from an ancestor.

Hello, John. Welcome to Straight Razor Place!

The simplest answer is to go to Straight Razor Designs and buy a kit. You will be able to find one well under $350. You could also buy a razor in the classifieds her at SRP.
I also encourage you to read the advice for starting out in the library here at SRP.Beginner's guide to straight razor shaving - Straight Razor Place Library

+1 on the Ralf aust razor
+1 on the castle Forbes lime shaving cream

Yep. Robin has just made some great choices for you there.

In the Castle Forbes line, the lime is my least favorite. To me it is reminiscent of green Lifesavers. On the other hand their Lavender is one of my favorites. In the lime scent I prefer Truefitt & Hill West Indies Lime. YMMV

Might be worth picking up two razors to get up and running. One of the vicious circles when starting out is premature dulling due to less than perfect shaving, stopping and maybe honing technique. Two razors allow you to continue shaving whilst one is out for honing or as you learn to hone/maintain your edges for a comfortable period of time.

Beyond a smooth piece of leather and a razor edge honed by someone who knows what they doing a large percentage of what follows is personal preference. There are a few vintage shave ready razors in the classifieds well within budget. Tony Miller makes very nice strops, if buying from a strop maker it might be worth asking if you can get a very basic starter strop too, first to get you into the rhythm and then later to apply abrasives as a touch up strop. My preference is for a narrower strop.

Consider posting a photo of your great grandfathers razor, it may just need a trip to the hones.