There are many ways to build a hybrid. I go pure stats, so I have str/hm/dex armors and str/int dex/hm charms.
The cheapest way to build a full chaining hybrid would probably be this:
Weapon: Highest ee possible.
Armor: Highest ee possible with int/hm or melee stats (ee is most important here)
Charm: Either hybrid charm or pure melee
Acc Slot: Highest ee possible on a heal charm.
Now for some useful adds: Life Steal (probably your most valuable side mod here to help you full chain), MPA, MPK, and Mana Syphon.
Keep in mind, you will need a Life Steal mod to help you maximize your build and will make up for inadequacies with your heal charm or other items.
Although I've never tried it this way, keep in mind that it will take a while to kill mobs if you want to full chain. You're probably better off going pure melee items (unless you already have some of the aforementioned items) and then shrining your way through if you're on low life/mana.