Sorry, this is too long for a comment, and there is the beginning of an answer in it, especially if I get more info from the OP.
Can you define "cheap"? Sub $5? $10? $120? $50?
And, what does "Arduino input" mean? Pin comparability? Code comparability? sing he Arduino IDE?
For instance, ESP32 comes with BT & WiFI out of the box, and is certainly cheap, even with that memory. Some (a few, not the majority) have Arduino pin compatibility, so can take an Arduino shield - which would allow you to add Ethernet.
Raspberry Pi Zero W is cheap enough, if you need Linux, as is Orange Pi. Both have Arduino shield compatible HATs, allowing them to use any Arduino shield. They can also be made to run Arduino sketches (code).
E.g Raspberry Pi to Arduino Shields Connection Bridge