There aren't 7 tower types.  There are 5 placeable towers with 7 levels of upgrade each.  There are also the pre-placed vortex towers in a few levels.

Blaster:  Single shot guns that do low damage, upgrades to multiple shot guns for more damage.  Level 7 upgrade turns it into a sniper tower, huge range and damage but low firing rate.  Best used as cheap way to path creeps.  Level 7 blasters can target Replusar (donut) creeps.  Other levels can hit them sporadically, but most bullets will simply be sent off.

Shock Tower:  Slows down creeps it hits.  Each upgrade increases the number of creeps it can hit at once and the amount of slowdown.  Level 7 comes with a large range increase.

Missile:  Does splash damage.  Upgrades increase damage and firing rate, at level 4 missiles acquire the ability to re-target if their original target is destroyed before it can get there.  Level 7 missiles have huge range but incredibly slow firing rate and will not attack creeps before the missile loops around once or twice, but are smart enough to attack the closest creep to the exit.  Level 6 missiles are generally considered far more useful because they attack approximately 3x as fast and more directly.  Cannot hit repulsar creeps.

Laser:  Shoots "through" enemies to damage everything its beam hits.  Most useful when attacking a straight line of creeps.  At level 3 or higher you can lock the tower into a direction by double tapping it.  Level 7 comes with a large range increase.  All levels of Laser can hit repulsar creeps.  In Hard 4 (Crazy Ivan) there is a creep that Lasers actually heal rather than do damage, but it only appears in this level.

Thumper:  Shockwave attacks every creep within a 1 hex radius (ignore the blue range circle).  Most useful on an endcap where it can hit 5 hexes at once.  All levels of thumper can hit repulsar.

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Vortex:  Drag a line from a tower to a vortex to connect them.  Vortex will collect dead creeps and use it to power up towers for bonus damage.  You cannot place a Vortex tower in Swarm, it has to already exist in the level.  Double tapping a vortex will make it explode.

Geodefense is one exciting game and is mainly action oriented but there are few stages where we get puzzled up like that in most puzzle games but the perfect power will surely help to break the towers and as Elysium has discussed about it, it's great to use it and now the game is just exciting at every level.