As for my experience, a minimal requirements are:
- fast single-core or recent dual-core CPU 500MHz+
- 512Mb of RAM
- 100MBit/s ethernet card
- 4Gb storage
- Linux kernel v4 or recent FreeBSD minimal distro
As a sample you can use yourself - it's a Raspberry Pi 2 - cheap and decent one. From ARM single-board computers, however, I do recommend to use OrangePi or BananaPi - nearly-same price, a way better hardware( like Allwinner H3 quad-core CPU and 1Gb+ RAM).
If you describe your task more specifically - I'll be able to advise you better and help you to set it up
So as for the task you have described, the proposed solution is:
- A single-board computer, I do recommend OrangePi Prime with a power usb cord(included in link above). I'm using the predecessor of it's predecessor - Orange Pi PC, still working, very good and fast. Well, you can pick Raspberry Pi 2 or 3 - but it will cost you the same and be a way slower in a "horsepower".
- A heatsink for single-board computer. If you choose any of the SBC's - all of them do have CPU, and like any CPU it needs cooling. I was starting using cooling from Deepcool NBridge2 chipset coolers, then found this chipset cooler. You can pick any of them - they're absolutely equal, both tested. To properly fit it on the SBC CPU and it's surrounding chips - just use an iron file to cut off the extra parts of "iron pad" of the cooler. Place it to cover the CPU and to mae no shorts - thermal grease of a good quality is included in both cases. A word of warning: do not buy cheap/tiny passive coolers for SBC's - you'll make it short-living and slowing itself down because of overheating! This chipset cooler costs 3-5$ above them, but it's worth the price, the difference is huge
- A USB 5-to-12V step-up adapter - to fire-up the cooler, you'll neet 12 Volts, USB has only 5V, so - there's a lot of power converters e.t.c., I'm using this one - works for 1.5+ years, no problems at all, powers up 2 NBridge 2 coolers all this time 24/7. If you do not plan to have any additional SBC's, then you can just solder a cooler's wires to this adapter and be fine. If you do plan or "maybe" to expand the number of the coolers powered - take this splitter pack and make a jack with pins to be connected to the power adapter - and just plug the cooler(or coolers if multiple) to the adapter.
- A patch cord - it's up to your taste! use a decent Cat 5e one - and be just fine about that! you put it to the place where your router stands, so it will work 24/7 eating 5-7Watts per hour and always ready for your requests. just plug it into your router - and you're done!
- A 2-port USB power - or 1 Port - use ANY normal usb phone charger capable of giving 2-3 amps. If one port charger is used for case with one sbc - then just plug 5-to-12v into the board's USB port and power up the USB power cord(included with SBC I've linked, for Raspberry Pi see the cables). Apple charger from iPhone 4s was just fine, for example. If you'll have multiple boards - take a look at multi-homed USB chargers: you need just a regular one with at least 2-3 amps per outlet. For big quantities of boards I do recommend this Multi-port docking charger, for small amount(1-3) of SBCs take a look at smaller multi-port chargers.
After the hardware part is done - just install minimal Debian on it, and tor node as well - and that's it! If you need further help - just drop me a line!