There are definitely $100 grinders recommended in this sub (Baratza Encore and Capresso Infinity are both just over $100 and can go on sale)
Bonavita brewer - $131.96 (or newer model)
Capresso Infiniti burr grinder - $84.95
Hario Scale - $42.91
Bamboo filters - $6.88
Total: $266.70
This is more or less the setup that I use every day both at home and work, and is why I almost never bother making pour over anymore. A good starting point is 1000ml water with 60g of medium grind (start there and tune grind to your preference before tuning water/coffee amounts).
To me the grinder and scale are the most important parts. If I could only get two items, it would be those (and good beans) and I'd tolerate an old mr coffee until I could get a better brewer. If your grind is inconsistent and old (pre ground), even the best coffee brewer won't be able to help. Having used both the Capresso Infinity and the Baratza Encore extensively, I slightly prefer the Capresso. Don't get me wrong, they are both great and will get you where you are going, but the Capresso is a faster grind and easier to clean by (only) minor amounts.
You could even throw in a Goose neck kettle and coffee dripper to experiment with pour over.
Something else to consider is a airtight storage container. I particularly like these - they keep your beans gooey/oily and fresh for weeks if you don't drink all your beans within a week of getting them.
Happy brewing!
Edit: words, grammar
Your best bet is to get a burr grinder and coarsely grind your own freshly roasted beans from a reputable roaster. I highly recommend the Capresso Infinity as an entry level grinder. It retails for $90, but you can probably find one for $60 if you look hard enough. And if you want to go cheaper than that, /r/Coffee can probably suggest some less expensive (though possibly manual) options.
For roasters, try any of the following: Blue Bottle, Coava, Counter Culture, Four Barrel, Ritual Roasters, Sightglass, Stumptown, Verve, or Water Avenue... And there are many other great options aside from these. They're just the ones I can think of off the top of my head.
Another option: If you live near a good coffee shop that roasts their own beans or sells one of the above brands, you can buy a bag from them, have them grind it for you, and then take it home and put it in your Takeya right away.
Seriously, the difference between freshly ground beans and pre-ground beans is like the difference between filet mignon and a turd sandwich, so give it a try!