How to delete vertices inside/merge two objects?

Greetings,
First post and I just picked up blender about a month ago and learned a lot just from reading through threads. But something I noticed I want to do a lot.
Im learning to model to fully utilize my 3D printer. and I have modeled a few things already and gotten my feet wet.
So what I was wondering, is there a “better” way to delete vertices that go inside an object? for example, I have a cube that i want to have a cylinder on top, like a LEGO piece if you will. What I want to do is move the whole cylinder into the top center, popping up a bit. I read that having vertices inside can be a bother later on. Is that true?

This is what I have been doing that I saw on a tutorial.

I have the cylinder hovering above the cube. CTRL+J and delete faces on top of cube, then edge select and F to make a face, then drag the cylinder down to level the top of the cube. I also heard “bridging” works faster but I havent tried that yet.

But can I leave the cylinder inside the cube? or make a loop cut on the cylinder to level the top of the cube and delete the vertices inside the cube? i dont know, just a idea, Im still new to this.

http://i1110.photobucket.com/albums/h460/TakaPhotoartistry/Screenshot%202016-01-28%2018.22.31_zpsc9cuve8j.png

Depends what you are going to do with it.
When you render it does it look as you want it to look ?
Intersecting geometry should be ok in most cases

Oh ok so for the sole purpose of 3D printing, what ever I see in a render, will be ok?
Of course as long as there’s no holes or thin parts.
So it just needs to be joined and doesn’t matter if I just slide a object into another?
I recently been playing around with the boolean mod but sometimes work with ngons (which I was told is hard for beginners) and doesn’t work