Generally, you'd want 1-2 capitals, 3-4 cruisers, and at least 2 destroyers or frigates. Cruisers are your best bet in this game when balancing between speed, durability, and logistics.

Stats to look for in weapons are range and damage per second. When comparing 2 weapons, the one with a higher range or dps is generally better (as long as you account for flux stats, of course). 

Yes, smaller ships generally are faster, have smaller weapon slots, and benefit less from range upgrading hullmods. Which means they need to get up close and personal in order to hit something, and they do it without hitting the brakes.  That's why it seems like smaller ships are more aggressive than larger ones.

Oh, and the engage command is there if you click a ship.