If you want longevity, you need to consider migrating to an AM4 (Ryzen) platform (AMD platform released this year). Your current FM2 platform is already outdated/end-of-life with no upgrade path (which means spending money upgrading the CPU on the same platform is not worth it).
Problem is, changing to a different platform that is more upgradable in the long run means buying a new CPU, new MB, AND new RAM (DDR4 RAM). The $50-$100 budget is not going to cut it for what you intend to do.
In an ideal AM4 (Ryzen) build, considering upgradability, you'd be looking at costs in this vicinity (upgradable to better Ryzen 5 or Ryzen 7 CPUs):
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD - Ryzen 3 1200 3.1GHz Quad-Core Processor ($109.88 @ OutletPC)
Motherboard: ASRock - AB350M Pro4 Micro ATX AM4 Motherboard ($74.49 @ SuperBiiz)
Memory: Corsair - Vengeance LPX 8GB (2 x 4GB) DDR4-2666 Memory ($84.99 @ Newegg)
Total: $269.36
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-09-03 14:18 EDT-0400
Another familiar option (before the advent of AMD Ryzen) is to migrate to an Intel Kaby Lake (7th-gen) LGA1151 platform. Though this platform is ~2 years older than the Ryzen, getting a more affordable Intel 7th-gen CPU such as the 2-core/4-thread Pentium G4560 (to save on costs) would still allow you to upgrade to better CPUs such as the 4-core/8-thread i7-7700/i7-7700K in the future. For this build, considering budget, you can spend something like this:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel - Pentium G4560 3.5GHz Dual-Core Processor ($78.89 @ B&H)
Motherboard: MSI - B250M PRO-VDH Micro ATX LGA1151 Motherboard ($66.99 @ SuperBiiz)
Memory: G.Skill - Ripjaws V Series 8GB (2 x 4GB) DDR4-2400 Memory ($72.99 @ Newegg)
Total: $218.87
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-09-03 14:23 EDT-0400
In both cases, you should have at least a $200+ budget.