I would like to start running a full node so I can start building bitcoin/lightning applications, but my laptop doesn't have the storage to do so. Does anyone have any suggestions on how I can affordably run a full node? I was thinking of running it on a remote server, but I'm also not sure of what I should look for in a service.
Please do NOT run bitcoind on a remote server (I'm assuming cloud). This defeats the whole purpose of a decentralized network, not to mention privacy of being able to check your balances or broadcasting your transactions. Your cloud provider can always keep your ssh logs and any activity you perform on that server.
A better cheaper solution (other than pruned nodes, which I would generally refrain from recommending as it prevents you from validating the whole chain) would be something along the lines of Raspberry Pi as also suggested by others. You can follow the instructions here:
If you are not too tech savvy, you could buy a preconfigured Raspberry Pi with raspiblitz
You can reduce storage requirements by running Bitcoin-core in pruning mode
You can run it locally in prune mode like @redgrittybrick suggested, or you can look into renting a cloud server.
For example yesterday I created an AWS EC2 instance with extra storage and I played around with geth to deploy some smart contracts to testnet. You can do the same with bitcoind etc.
You will connect to these remote servers with ssh and execute terminal commands without wasting any hard drive of your local pc.
The cheapest configuration consists from RPi3 or its copy Opange Pi equipped with SATA shield for external HDD. I've used my old HDD which left after laptop upgrade with SSD.
I bought extension shield with metal case so everything is assembled together and the case has a fan.
This hardware is working for almost two years. During first year it had Core + LND, now it serves Core + Elects and fairly stable (for this cheapest configuration).