Shimano cross compatibility

Hi there. Can somebody please help me. Can you mix and match Shimano components across the ranges. I know you can use any 11 speed components together but what about the others. Basically I am looking at a new frame but want to swap my old components over. I can’t afford a new frame and groupset all at once so that’s how it has to be. I am running Claris but want to upgrade in the future. Also currently have a sure taper bb and un named crankset. I am keen to upgrade that to a better bb and crank set in he new frame but rather than get a Claris crankset would a tiagra one work with the rest of my Claris components for the time being? That way I can upgrade the other parts of the groupset as and when, ending up with full Tiagra on a nice new frame. I have already upgraded wheels and tyres. I know buying a whole new bike would be more cost effective in the long run but I don’t have oodles of spare income to splash out in one go. Plus I want to enjoy the process of building up a bike myself. If you can build it then you can fix it. 

If you're new please join in and if you have questions pop them below and the forum regulars will answer as best we can.