I dunno about Apple Arcade gaming, but an 8-16 GB 2014 will run Monterey well for word processing and Apple Music, after you upgrade to NVMe SSD (which is literally just a 10 minute hardware install if you have the right screwdrivers). I say 8-16 GB because you have to pay specific attention to the RAM when buying a used 2014. There are a lot of cheap 4 GB models available on the used market, but 4 GB is not sufficient and the RAM is not upgradable.
The 2012 has upgradable RAM, but cannot officially run Monterey.
For the time being, until the M2 / Mx Pro Mac mini models are released, my 2014 8 GB Core i5 dual-core Mac mini is my primary work machine, with Safari, Pages, Apple Music, Apple TV+, YouTube, Netflix, VPN, etc. Pretty decent. I bought a cheap model with hard drive only, and installed an NVMe adapter (< US$15) with 500 GB Western Digital SN550 SSD. I left the hard drive in place since it would have been too much of a hassle to remove, and I can use it for extra storage/backup, etc.