u/amanforallsaisons did a fine job. However, you're asking about amazon and looking for a budget deal.

The Dorco PL-602 is the most-affordable good DE razor.

The Body Shop synthetic brush is a plisson-type synthetic. I don't have one, but I know people who do. It looks good, and should be soft-tipped, and easy to use.

EDIT: let's go with one I do have: razorock plissoft

Soaps are a littler harder - do you like fruity scents or non-fruity scents? There are shaving soaps on Amazon (Razorock and WSP) but not in sampler form. You won't go wrong with soaps from either Razorock or WSP.

A blade bank I picked this as the add-on item rather than Prime, because it's cheaper and you'll have enough to make the add-on order work if you use your cart instead of 1-click buying.

Get a sampler pack of blades. I prefer tryablade.com for samplers, but if you wish to do amazon, this isn't all bad. The normal problem with a sampler on amazon is that you're getting blades from the same factory, so you aren't really getting a chance to sample well. Here, they're at least well-regarded blades, so it's not terrible.

Alum - if you hold alum to your face where you nick yourself, it will stop the bleeding.

Witch Hazel. A lot of people like Thayer's. You can use any witch hazel you like as an aftershave - I put this one here because I'm tempted to get it myself. lemon Thayer's witch hazel

Balm. Not strictly necessary, but if you find yourself burning, it won't hurt to have on hand. nivea post shave balm

Honestly? If you use shave oil, like Shave Secret (walmart), you don't need the brush or shave soap. Savings can be had if you're incredibly price sensitive. But many people prefer the brush and lather method.

Shave bowl. I use a collapsible bowl which is convenient for bowl lathering when I travel.