help with "mirro" finish on mahagony

[John S. Genzer]

I am a relatively new to workworking but have just finished several plant stands and a glass door display cabinet. I made these out of pine, walnut, mahagony, and hickory. So far my finishing has been simple with stain and poly.

Now I am going to build a secretary desk out of mahogony or walnut and wish to finish it with the old style "dark" mirror type finish. I do not have spray equipment. I have read a lot about this finish process and have several questions:
1. what is the best way step by step to achieve a mirror type finish without having spray equipment? And, product suggestions would be appreciated here also; do I use poly or shellac? Do I try something like BLO and no pore filler?

2. Do I need to apply the stain and then the grain filler BEFORE I assemble the desk (which will have small compartments for letters, bills, etc, and a drawer-so a lot of corners and joints where pieces come together)? Then apply the finish coats of poly after assembly? That just dosent seam right to me (but what do I know as a beginner but how well will I be able to apply grain filler into all the corners where pieces join if I do it after assembly? Any advice here would be appreciated.

By the way, I do this as a hobby-not for sale. The secretary desk is for one of my daughters.

Thanks for your help. In the past I have gotten some great guidence from this site while making those plant stands and that cabinet.
Thanks,
John