Moto E, G, etc.. Almost as cheap as chinese brands, but with much better update / software support.
Doesn't that depend on your carrier? IIRC some carriers detect tethering by looking for packets with different TTL values (which would represent different devices' defaults, or indicate an extra decrement as the packet went through the phone), or inspecting HTTP User-Agent.
You can hack around both TTL values and user-agent btw. Deep packet inspection, maybe less so
Also, DPI can be trivially bypassed by running all traffic from your phone through a VPN. All traffic, tethered or not, will be indistinguishable to your carrier.
VPN would work for DPI true, hassle though.