I am going to be putting cabinets up in my kitchen in the next few weeks. One wall is a block wall with 1x3 furring strips attached (my home is a twin and this is the fire wall between the houses). I am planning on securing the furring strips with 2.75 inch tapcons to the brick to support the weight of the cabinets and microwave. There are currently cabinets and a microwave hanging on the wall but I am changing the placement and adding more cabinets as well. The cabinets use a rail system, so after securing the strips I was then going to secure the rail through the drywall and furring strips using tapcons again which should sink 2 inches into the block. Does seem to be adequate support for the cabinets? Is there another fastener I should be using? Thanks!

Tapcons are great. Are you using a hammer drill? Today I screwed some 1" PT boards into concrete but used an SDS bit in a hammer drill.

I do have a hammer drill, just need to find it. I've been using a regular drill. The tapcons came with a drill bit to use. The brick tough, but it isn't terrible to get through like concrete.