There're a few different categories of units.
Rare Summon units are going to be your main units. They are only obtainable through the rare summon gate, and can be evolved up to six or seven stars, depending on the unit. You should keep all of them except for duplicates of a unit you already have. A lot of people have been salty because a unit that was previously garbage got a 6/7 star evolution that made it godlike (e.g., Shida, Elimo, Will) so I really suggest keeping them.
Jewel units exist to be sold, they give a buncha money but not much XP and are useless in combat.
Metal units (Elemental Ghosts, Kings, Gods, and Crystals) exist to be fused for XP. They give high XP when fused. Note that fusing a unit of the same element will grant 1.5x XP. Also, the gold cost of fusing to units increases as they level up, so once your unit is like level 20+ fusing ghosts may not be worth the gold expenditure. The gold cost goes down when you hit the maximum level, I'll go over why you may wanna fuse into a max level unit later.
Evolution Materials (Nymphs, Spirits, Idols, Pots, Totems, Bulbs, Tones, Mecha Gods, Mimics) are needed to evolve units. Some of them grant a fair amount of XP upon fusing too, but metal units are better.
Enhancement Units (Frogs and Imps) improve your unit's abilities. Imps increase their stats up to a point, and carry over when you evolve the unit. Sphere Frogs grant the ability to equip two spheres, and carry on when you evolve the unit. Burst Frogs/Emperors improve the unit's brave burst - more on that later. None of them grant a particularly special amount of XP and they don't sell for much. They are relatively hard to get, so use them on good units.
Lastly, mobs. I use this to refer to the spare units you get from questing, like slimes. These are usually 1/2 stars, but you may even get 3 star ones when you're farther into the game. Anyways, while they can be leveled up and evolved they're weaker than rare summoned units, and generally only go up to 4 stars at best. Their main purpose is to fuse into your rare summoned units for a chance at levelling BB.
Actually, one more type of unit. Vortex units! These are acquired from limited time vortex dungeons, such as the ongoing Miku event. These units can be about as good as a rare summoned unit. Some of them are definitely worth using until you're very high level.
OK, now that's out of the way, let's talk about levelling your Brave Burst (BB). Your BB has levels, you can see it when you're looking at a unit, right on top of the BB description it tells you its level. This level increases by fusing. There are three types of BB: Support, Healing, and Attacking. If a BB does more than one of these things, it will count as the highest one: Attacking>Healing>Support. What is a support BB? Basically anything that does't heal or attack.
Anyways, the reason this is important is that you get a chance to level your BB by fusing units with the same BB type into it. This is the main use for mob units. As your BB level increases, the chance of it leveling higher decreases. However, you can ignore all this "Chance" business by fusing Burst frogs! Each frog will give you a single BB levelup. A Burst Emperor will give five BB levelups.
BB levels are halved when you evolve a unit. So if you had a BB level 8 before evolving, it becomes 4 after evolution.
BB levels cap at 10. However, 6 star units can unlock their Super Brave Burst (SBB) by reaching level 10 BB. A unit's SBB can often be just a stronger version of their BB, but it can also be a completely different ability. SBB can also go up to level 10.
Lastly, 7 star units can unlock their Ultimate Brave Burst (UBB). It's a bit more complicated and since you're new you won't deal with it for a while. Basically you jump through a few hoops and then you can use a super powerful ability. It unlocks by reaching SBB level 10 on a 7 star unit, and cannot be leveled.
Think that's all I can tell you about unit types and fusing.