So far as I know:
*The value of a system is determined by the most valuable thing you have scanned in it. So if you have scanned a metal-rich planet there is no extra value from scanning an iceball. Similarly, if you have scanned one group in an asteroid belt there is no point scanning another.
*As Ziltoid points out, any objects detected by your Discovery Scanner appear as Unexplored entries on the destination list in the left UI panel. This is the simplest way to select them for travel.
*The other way of detecting an object is visually. Look for dots in the stars around you which appear to move when you are travelling in supercruise - those will be other stars in the system / planets / etc. Normally they are fairly close to the plane of the orbit circle for the star. However this visual method is very very slow (not a credit-efficient use of time, though it is fun)
* The surface scanner roughly doubles your exploration income. However, at 250kC, it is pretty expensive and also it still takes hundreds of systems scanned for it to break even.
* Personally I've found deep-space mining more lucrative than exploration. As an explorer you occasionally encounter the miner's Holy Grail - an unexploited system with a Metallic (not Metal-Rich, Metallic) asteroid belt. These rings have a high proportion of expensive metals like Platinum, Palladium and Gold. That makes more money than exploring!
I'm not sure what to recommend as an upgrade path as I started out with a Kickstarter-backer reward Cobra with upgraded drive and scanners. That ship works very well but the value of the intermediate discovery scanner, improved power distributor and FSD probably runs to 1M+ credits if you are buying it from new. Also a Cobra hull isn't hugely cheap.
I haven't played with the Adder, which is meant to be the first "explorer"-line upgrade on a par with the Hauler and Eagle. However I can also see a Hauler working OK, particularly if you wish to do some mining on the side.
