Don't forget that NPCs show up only during a certain time of the day. Some show up only during the day and others during the night, so you'll have to explore every city twice.
The inventory sucks butt because there's a limit on the amount of items of each class you can carry. Several times I dropped some trash (because my inventory was full) that hours later I needed for a quest.
The game is easy, so don't fret. Level (or level difference between your characters and the enemy) is the most important stat in the game, because it has a huge impact in damage dealt, received, accuracy, evasion and block. Any enemy, including the final boss, is a joke if you are six levels above it. If an enemy gives you trouble, come back later when you've gained a few levels.
Speaking of important stats, the second most important one is Agility. The game doesn't explain what it does, but it plays a role in both acuracy and evasion. Critical hit rate is also important because critical hits fill the party gauge.
Since I said that Agility is so important, you can guess that all the agility-boosting and weight-reduction (weight reduces agility) skills are important to learn. All the AP boosting skills too.
In my game, all my characters except the last two to join (or the last three, I don't remember well) were able to learn all their skills, so don't worry about it. The same can't be said about the Arts, though (that's why I recomended to learn and link to everybody the AP-boosting skills).
Characters can learn up to two extra skill trees. The way to unlock them is to complete certain quests.
If you want to have an easy time crafting gems at the end of the game, don't raise the affinity of one of your characters (decreasing affinity is a pain in the butt). The last character to join is the best one for this purpose.
As for which arts to level up, it depends a lot on the way you want to use the characters. You're really early in the game, but I'll say that I still used Shulk's Back Slash a lot at level 99 (and Shulk isn't too versatile).
This game has missables. There are entire areas that can't be accesed after a certain point, which means that you won't be able to fight the unique monsters in them. Defeating those monsters is the only way outside of leveling up to obtain affinity coins, which are used to link skills from one character to another. Until certain events in an area called Mechonis Fields happen you can't miss any of them.