Would it be effective for larger nations to give much of their income to smaller nations perhaps?
Also, how worth it is it to push for crates after the first buy, when should I switch over to doing that instead of building free hospitals for the people.
Yes, that's primarily how wars are won. Since large nations rarely go to war with other large nations, they just fund their allies who are at war with troops and cash. Don't expect to get this big if you don't join an alliance though, because once you start hitting 500 GDP a lot of people are in alliances. Once you hit 700 GDP EVERYONE is in an alliance, and they'll all be looking to attack non-allied nations for a quick GDP boost.
Right away, WW1 Tech is vital if you plan on declaring any wars (Which you should to quickly boost GDP.) After you get your crate, then save up for a hospital for a quick approval and QoL boost. Once you get your stability and approval to the highest level, you don't really need to put anymore money into those because they'll pretty much just boost each other each turn for being high.
You can start focusing on getting WW2 tech once you get to 600-700 GDP, and it requires 40 Lee-Enfield crates. You should keep track of how many you're buying, and spend a majority of your GDP on crates once you get to this point. Also keep in mind the QoL drops faster the higher it is, and drops every two turns. It's not necessary to keep it at maximum, because at higher GDP's it's a massive money sink, but if you keep it at around average then it'll drop relatively slowly and allow you to easily boost it back up with the cheaper QoL policies.