Reddit mentions of Desktop Mini PC Fanless Computer Windows 10 Pro Intel Atom Quad Core x5-Z8350 4GB DDR/64GB eMMC HDMI and VGA Port 2.4/5.8G WiFi BT4.1 USB 3.0 Mounting Bracket Auto Power On

The cheapest way is to just run Bitcoin Core on your daily PC for a few hours a day(after downloading the blockchain) to help the network or if you can let it run, just leave it on. Once you download the ledger you can start accepting connection on Port 8333 so open port 8333 on your router so you can accept transaction updates to the ledger.

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To run a separate system that you don't need to build a whole PC for you can get a MINI PC. They can run from around 100 USD. The specs are what you want to consider. The cheaper you go the less you'll get. like I said anything over 2GB of Ram, a Celeron processor and at least 500 GB storage to start should be good. Upping your HDD space will be the only future purchase. Probably should get a external since it will be easy to bounce the Bitcoin data from a small HDD to a bigger one at a later time when you run out of room. current size of the block chain is around 300GB i think.

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You might not be able to get a mini PC with a decent Processor but here's a decent start. https://www.amazon.com/Fanless-Desktop-Computer-Windows-Mounting/dp/B07QY8LDGX/ref=zg_bs_13896591011_10?_encoding=UTF8&psc=1&refRID=BKDSFWSFC4043GVBYNDJ

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here is a bit of a better one with Ubuntu already installed. Still a weak Processor though.

https://www.amazon.com/ACEPC-x5-Z8350-Computer-Ethernet-2-5-Inch/dp/B07WCF1GKR/ref=zg_bs_13896591011_4?_encoding=UTF8&refRID=BKDSFWSFC4043GVBYNDJ&th=1

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Also running on Windows is ok and will work fine. But Linux Distros like Ubuntu are lighter and most times faster less resource hungry. You DONT have to, but it really helps because there wont be any bloatware with Linux and it wont do anything you don't want it to unlike windows with their crazy updates and bloatware apps you wont use. Also most Distros will ask if you even want to install 3rd party applications so its nice to have the option to exclude programs that would otherwise just use up resources.

Things to note:

Running a node is fairly straight forward you should Read thoroughly here https://bitcoin.org/en/full-node because if you run a node and do not finish downloading the blockchain and do not accept connections on 8333 you will essentially be doing no good for the network. Also broadband speeds are a must since you will essentially be dedicating some of your bandwidth to the Bitcoin protocol. It isn't much, but I run a Network monitor on my PC, and over a week the node used around 50-60GB depending on the activity on the blockchain. that's not much but on metered connections you will blow through any Data caps from your ISP, especially if you use your network for other things like video streaming.