Reddit mentions of Fendrihan Synthetic Shaving Brush with Black Handle for Personal and Professional Shaving

Comparing badger, boar, and synthetic brushes is like comparing apples, oranges, and bananas. One isn't better than the other, they're just different.

Synthetic. This is the most practical option, but the one I like least. Synths make lather very efficiently, tend to release it well, and the good ones are extremely soft. But to me the face feel isn't as good as what you get from a high-quality badger or boar. Also, you've expressed a desire to avoid plastic products, and synthetic bristles are made from nylon.

Boar. Buying a boar brush is like adopting a puppy - you need to know what you're in for. They're the only brushes that need to be broken in. Basically, each bristle in a new boar brush comes to a coarse point at its tip. With time and use, the tip will split, just like a human hair. The fibers at the tip will get finer and softer, and the brush will become more effective at building and holding lather. You won't ruin a boar brush by failing to break it in, but it won't be very good until you do. As it breaks in it will become increasingly soft and the performance will improve dramatically. One thing to keep in mind is that many (most) guys prefer a boar brush that's been soaked for a few minutes so the fibers soften up; this is only an issue if you're the type who forgets to soak the brush. I am.

Badger. While I appreciate what a synth has to offer, and while I love my boars, if I had to choose a single desert-island brush it'd be made with badger hair. Which one I'd pick will change from time to time, but not what it's made of. There's no such thing as "silvertip badger." Badger hair terminology isn't standardized, and grading is not regulated. All the adjectives used to describe badger hair are basically marketing terms. Ignore the puffery and just get a great brush.

The best way to make sure you do this - regardless of whether it's badger, boar, or synthetic - is to buy one that's made by a reputable manufacturer. If you're going to buy a no-name or store-brand brush, get it from a vendor who's known to be reputable within the wet shaving community. Etsy vendors tend to just make handles; they buy (almost always mass-produced Chinese) knots and glue them in. So make sure you know where the knot comes from.

I totally disagree that a badger brush is a bad choice for a beginner; they perform well out of the box, and a good one is easy to use. Given your budget and the preferences you expressed, I'd recommend the Semogue Owners Club 2-band. The quality of construction is high; the knot is hand-made by artisans in Portugal, and the wooden handle is turned there as well. The hair used is very nice, with soft tips and tons of backbone. And IMO it's a steal at $57 (the price in the link I provided). MSRP is around $100 and the best price is usually $70 or so. The SOC is the least expensive of the badger brushes I have in my rotation, but I recommend it very highly.

A Semogue boar would be a great second brush, and it can't hurt to have a synthetic - some people actually prefer them to natural fiber. You can get a 1470 for $11 and a Fendrihan synth for $12, so the risk is minimal and the total cost is still within your budget.

If you're set on buying from amazon, you might want to switch out the brush to a cheap synthetic like this or a cheap boar brush from semogue or omega.

I transitioned out of cartridge shaving a few years ago but only in the last year and a half started using the soaps and the brushes. And I have to be 100% honest with you it makes a HUGE difference. Get yourself a cheap synthetic brush like this Fendrihan which I adore and yes that's me as the only review on it. Or even this Razorock either would be wonderful and cheap choices. And then just snag a soap that you like the scent of it'll last you years. And your all set. One thing I personally highly recommend is doing this Sterling Starter kit it's perfect for someone just starting out imo. You get a razor some nice not aggressive astra blades and some soap that will last you quite a while.