I appreciate both Bitcoin and the Tor network and would like to do my part to help.
Is there anyone that can help me set up a computer that will just be dedicated to running a Bitcoin node (I think that's what I am looking to set up) to help verify transactions.
Download Bitcoin Core from
https://bitcoin.org/en/download. Install it, and run. You are then running a full node. To further help the network, you can allow incoming connections. Check your firewalls (on both your computer and your router) and make sure that they allow port 8333 and are forwarding it to port 8333 on the machine running Bitcoin Core.
Also if possible I would like to set up a Tor relay on the same machine.
It is possible. If you are using Ubuntu/Debian, follow these instructions:
https://www.torproject.org/docs/tor-relay-debian.html.en. You can also look at the instructions at:
https://www.torproject.org/docs/tor-doc-relay.html.en for some more info on setting up a relay, especially the torrc file.
As a bonus you can also setup Bitcoin Core to also go over Tor and accept tor connections as well.
Some questions I have are:
Is it possible to do both effectively and efficiently on the same machine?
I don't see why not.
What would the requirements be to do it the best way that is feasible for the average joe?
Setting up a tor relay is kind of difficult for an average joe as it typically involves linux and command line. Bitcoin full nodes are super simple as it is just download and install Bitcoin Core.
Would it use a considerable amount of my bandwidth?
Yes. Bitcoin Core will use a lot as it has to download the blockchain, which is quite large, and keep in sync with it by downloading and uploading to several peers.
What would the maintenance be for something like this?
Practically none. Just make sure that the computer is still on and that both pieces of software are still running.
Bonus question, would there be any personal benefit to myself by running something like this, i.e. being able to confirm my own bitcoin transactions faster, or will I be able to collect some transaction fees? Not that its necessary for me to benefit from doing in order for me to do it. I will regardless, I just want to make sure I take advantage of any pros that may be available to me for doing such a thing.
Thanks for your help. As you may have guessed I am not the most computerly savvy, so it would need to be a dummies guide.
There are no benefits like that for running your own full node. You will not get any sort of monetary compensation and your transactions will not confirm faster. What you do get is the security of a full node and an accurate estimate of the optimal transaction fee to get faster confirmations.