The new players I play with in co-op arena/conquest tend to have weird item buys. It's totally okay to stick with auto-buy for the first day or so. When you get a little more comfortable and familiar with the game, start buying items in order off of the popular items tab. Start with boots (unless in conquest, where you start with an 800 gold starter item) and then work from there.

From there and as you go along, you'll learn which characters/classes build which items. Hunters generally build attack speed, critical hit items, and armor penetration. Guardians like aura defense items, cooldown reduction, personal defensive items, and health. Mages like power, penetration, and cooldown reduction with a health or defensive item relatively soon after buying boots in order to boost survivability. Assassins generally like cooldown reduction and a mix of offensive and defensive items. Warriors tend to build cooldown reduction and defensive items with a hint of power.

That's the basics of items. Best of luck!