If you want to make a couple million credits purely by exploring, you can do it without having to leave inhabited space. True, thousands of CMDRs have been there before you, so it's not really true "exploring", but it still pays the same, and you still get credit towards your exploration rating. You'll want to buy a Detailed Surface Scanner module as soon as possible, too (cost about 500,000 credits); this greatly increases the value of the scan payout, as well as giving you better info on the planets being scanned.
First, find the star TRAPPIST-1. It's only a couple dozen LYs away from Sol, so if you're near the starter systems, it shouldn't be too far away. It's a small red dwarf system with an uninhabited Earth-like plus a bunch of other nice valuable planets; it should get you about 700,000 credits for the whole system. Best of all, every planet is within the 500 Ls sphere of the Basic scanner honk, so you should be able to find them all without difficulty. Just point your ship at each planet in turn until the scan completes. Now you can travel 20 LYs away, sell the data and you can afford to buy an intermediate scanner. You can then go back to TRAPPIST-1 and rescan the planets with the DSS fitted for extra money, or hold off and go immediately to Step 2.
Step 2, my next recommended target: Fomalhaut. It's also quite close to Sol. It has an inhabited but Unexplored Earth-like planet 2300 Ls from the star. This is outside your Basic scanner range but fortunately, this planet is inhabited and has a space station around it: Dobson Terminal. And space stations are always visible on your system map and navpanel, even if the planets they orbit are not. Jump into the system, scan the star, then head out to Dobson Terminal. Once you get within 500 Ls of Dobson Terminal, honk the scanner, and the planet should appear. Now select the planet and fly up to within scanner range (about 50 Ls) of it to scan it. Feel free to repeat the process with the other inner planets in the system with space stations around them, though they're airless dragon-spittle blobs of rock nowhere near as valuable as the Earth-like.
Travel 20 LYs away from Fomalhaut, sell the data and you should now have enough cash to buy an Advanced scanner. After all that jumping around, you might have some additional data to sell, too, so maybe you can already afford a Detailed Surface Scanner or a better drive. Anything is better than your default drive, so long as you don't downgrade the size (keep the number the same). If "running away" is your preferred combat style, you can always sell your weapons to lighten your ship for extra jump range.
Next targets: up to you. I'd suggest going out to the fringes of inhabited space, switch the galaxy map to "Map" mode, select "Economy" as the sort parameter, and search for Terraforming economies (in Economy Map mode, they are dark green on the galaxy map). Pretty much any one of those dark green systems will be under 1 million population (and therefore Unexplored), with at least one terraformable or Earth-like planet somewhere in the system; these systems should be worth at least half a million each. Scan as many as you need until you have enough cash to buy a decent exploration ship (I'd recommend either the Asp Explorer or Diamondback Explorer) and fit out your long-range deep-space explorer properly.