Novatroopers are shock troopers, great for storming heavy anti vehicle defenses or inserting deep behind enemy lines supported by Plex soldiers. On some maps with a great deal of narrow spaces and verticality, such as commenor, where trying to move AT-ATs across the map can be suicidal, I will insert them into reinforcement points using IDTs to take positions and allow my heavier stuff to land and destroy enemy base buildings. IDTs are also good at supporting units on the ground in situations like this. They're decent against air units and can do well against enemy infantry and light vehicles.
As for space, I am a Tector fanboy, they may not carry any fighters, but they have massive firepower and durability, and are fantastic at absorbing fire and tearing apart enemy ships in combination with Lancers and other frigates. Tectors go out front, weakening larger ships and usually crippling small frigates very quickly. Lancers can go close behind, with Victory IIs and other small frigates can support them against large ships.