Some of my machines:
Workplace desktop: Dual-core Pentium G840 2.8 GHz (PassMark 2586), 4 GB RAM, HDD, Win 7. Surfing on it is mediocre. Too much disk thrashing.
Home desktop: Triple-core Athlon II X3 435 2.9 GHz (PassMark 2485), 8 GB RAM, SSD, Win 10. Surfing on it is very good.
Home desktop: Quad-core Core i7 870 2.93 GHz (PassMark 5459), 12 GB RAM, Firewire 800 SSD, Mac OS X 10.11. Surfing on it is very good.
Home desktop: Dual-core Core Duo 2.0 GHz T2500 (PassMark 876), 2 GB RAM, HDD, Mac OS X 10.6. Surfing on it is poor, for multiple reasons.
Home nettop: Dual-core Atom 330 1.6 GHz (PassMark 596), 3.12 GB RAM, SSD, Win 10: Surfing on it is absolutely horrible.
Home laptop: Dual-core Pentium SU4100 1.3 GHz (PassMark 873), 4 GB RAM, SSD, Win 10. Surfing on it sucks.
Home laptop: Dual-core Core 2 Duo 2.26 GHz P8400 (PassMark 1471), 4 GB RAM, SSD, Mac OS X 10.11. Surfing on it is OK.
Home laptop: Dual-core Core 2 Duo 2.4 GHz T8300 (PassMark 1493), 4 GB RAM, SSD, Mac OS X 10.7. Surfing on it is OK but is limited by lack of hardware GPU h.264 decode and limited browser support.
What does this tell me for web browsing?
1. Slow CPUs are bad, but higher clocked CPUs even from 5 years ago are fine.
2. HDD bad, SSD good.
3. 4 GB not quite enough. 8+ GB needed.
4. On a Mac, you need one of the latest iterations of OS X for proper browser support.
5. You need hardware h.264 decode support.
Given these results, I'd say any current desktop Core i3 would be fine for surfing, and as long as you have a modern OS, 8+ GB RAM, and SSD.