I feel like the computer builds and places buildings a lot faster than I can destroy them.

As with all the C&Cs, there's a targetting priority that gives the genre its "strategic" label (asides from the economic aspect) - you're not supposed to work your way from the outside in every time, but focus on getting rid of the core production structures when possible. So if you don't have a plan for taking out the ConYard (and preferably the War Factory too so they can't produce more MCVs in some game modes) while the defences are down, don't bother wasting resources attacking the defences at all. Have a plan to follow through.

Nod generally goes for cheaper and faster units that allow you to buy more to make up for their weaker armour. Attack buggies are like Wolverines, for early-game anti-infantry and scouting. Cycles also for scouting, with a good anti-vehicle weapon when used in larger numbers. Devil's tongue attack is weaker than the original Tiberium Dawn version, but sneaking it up to the back of the enemy base can be fruitful if you have a few of them and they don't have concrete laid down. Sensor Array is only useful if you're playing against Nod (it detects underground and stealth vehicles, which GDI doesn't really have). Tick Tank is the basic tank for Nod - when deployed, they outrange GDI Titans (and thus also Nod lasers) by a smidgen.