Once you've researched Alien Alloys, you will be able to research Personal Armour, which is a vast improvement to the standard coveralls.
While serving as a vital upgrade to the pitiful defenses offered by an unarmored X-Com soldier, personal armour is only mildly effective against weapons like the Heavy Plasma you'll end up facing in later missions, though it can often withstand a single frontal hit if you're lucky. Personal armour is also inexpensive and fast to produce, and since you often end up with huge stockpiles of alien alloys, you will seldom run out of materials to build the armor with.
This armor should see heavy use until you can build the Power Suit, which dramatically outperforms the personal armour.
Due to a bug when units are spawned, soldiers wearing Personal Armour are treated as though they are wearing Power Armor when damage modifiers are applied -- but a Power Suit or better is needed against stun damage from smoke.