For a home use server I'll choose the i3. Have had an i3 in a desktop once (later upgraded to i7 mostly because the need of running virtual machines). The i3 worked surprisingly well, and at very low power, the fan was staying off most of the time. I don't recall any problems with Linux switching the Intel power levels.
For a home use that is on 24/7, you may want to consider the cost of electricity, and the noise from the fans. A dedicated rack server makes an unbearable noise, and it is way more power hungry than an i3.
RPi is not a good option, it has considerably lower performance in network, disk and memory bandwidth. For a server, good data throughput is much more important than the CPU speed. The CPU bottleneck usually happens later, under heavy load with many parallel requests (usually from a swarm of users), while the bandwidth data rates (between various internal parts of a PC) can be reached even with a single user.
So, unless you want to sacrifice performance for a lower power bill, I won't think of RPi as a long term server solution. Though, if that is what you already have, a RPi can be a file server, as long as you are the only user and don't care much about high speed transfers.
Can't comment about N100, never used one.