MHC I is on all nucleated cells in the body. MHC II is only on antigen presenting cells (APC). So APCs have MHC I and MHC II.
MHC I signals CD8 (Killer/Cytotoxic) T-cells and MHC II signals CD4 (Helper) T-cells.
Memory T cells are just T cells with a "memory" of how to respond to an antigen.