A 6" mirror with a focal length of about 15" will be a F2.5 which will be a very difficult scope to build and get any real quality with it. In addition, the magnification may be a bit more than you wish as you eye will have a opening of about 2-3mm at the most and the objective is 150mm which means that you need to have at least 50x (probably 75x or higher) in order to use all of the objective in the daylight. At night, the eye will open to about 6-7mm which means that 25x will be pretty much the minimum magnification that will be needed to use all of the objective.
The next problem is that the shorter the focal ratio of a mirror, the harder it becomes to shape it into the proper parabolic shape (for a Newtonian design which isn't too hard to build) with enough accuracy to enable maximum magnification of the image.
Cassegrain designs will end up with nice short tube lengths that you desire and also the nice eyepiece at the back end of the tube but end up with nasty problems of making a convex surface and measuring that. There is one design of the Cassegrain, the Gregorian design which uses a concave secondary but it ends up having that secondary out past the focus point of the primary. Being a concave surface tho allows the secondary to be tested without having to resort to fancy extra optics to get the shape of the surface right.
Again, you might as well build the scope so that a longer FL eyepiece will provide that minimum 75x magnification and you will be able to obtain as much as 300x before the view starts to seriously degrade if you make the scope well enough.
Another little fact is that terrestial scopes have a built in inverter for the image so that things look right when you look through them. Astronomical scopes don't do this (we're more interested in the light than where it is at the focus as there is a 8% or more hit in light loss everytime that you hit a surface) and the Gregorian telescope is the only one that provides an upright correct image.
There are a fair number of websites that describe making optics and they all go through the process fairly well although there are some minor differences in how it is done.