Hey Psychic Donuts, welcome to the forums and to Elite Dangerous.
First, note that you can always go back to the stock Sidewinder whenever you die, even if you have bought another ship (you just won't get that ship back). This is a very good option for when you are starting out, because it means failure is cheap. When you are buying and outfitting a ship,
always remember to have enough credits for the insurance ("buyback"). You can see this on your ship management panel (the right panel). If you don't have enough credits, you'll be forced to go back to the Sidewinder whether you want to or not!
A Planetary Vehicle Hangar is a module that you need to install into your ship through the
Outfitting screen in Starport Services. This function is available at most but not all stations. You can discover if a station has the outfitting service by looking at it in the System Map. Also, note that not every station sells every module. The best place to outfit your ship is in a system with a "high-tech" economy. You can
search eddb.io to find the closest system/station to you that currently has Planetary Vehicle Hangars.
Note that each module compartment in your ship comes with a limited size. The Eagle is a very small ship. Planetary Vehicle Hangars start at size 2, so you will have to swap out your size 2 cargo rack or size 3 shield generator! I'm sure people
have used SRVs with Eagles, but I don't think it's the ideal ship for that task.
My recommendation is that you take that Eagle and do some bounty hunting, if you feel up to it, and save up enough credits to get a slightly larger ship that can hold a hangar without sacrificing too many other functions. I am particularly fond of the
Cobra Mk III. It is a very versatile ship and will serve you well. But even the Adder or the Viper might work too.
Here is a video explaining the basics of outfitting. Note it's pre-Horizons, so some of the details have changed, but you'll get the general idea of how it works:
Source: https://www.youtube.com/watch?v=xI8VhqA0DPk&nohtml5=False