For your Frameshift compartnemt, an A rated drive that is the largest number you can fit in your compartnemtn gives the best range.
There is an unofficial website called ED shipyard which is useful for testing out lots of different loadouts and gives you range and so on for any drive that you fit.
If you want to go exploring, you have to make many many jumps within the maximum single jump range of your ship, and you'll need a fuel scoop because you'll be going outside of populated space so you won't be able to refuel at stations. You'll also need a repair module, and preferably an advanced discovery scanner and a detailed surface scanner.
If you are in the basic Sidewinder ship you might want to do other things and make enough money to get a better ship before you go way out exploring. You can go exploring in a Sidewinder but it's certainly not the best ship for exploring.
One other thing to keep in mind is that if your ship is destroyed, you go right back to the last station you were docked at, losing all your exploration data in the process, so you need to be careful with your ship when you go way out into uncharted space.