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I can certainly understand the finances. Astrophotography & astronomy is expensive, for sure. I was recommending an EQ mount, as they are much more stable for larger/longer focal lengths. Even with the best equipment, getting good Astro images can be challenging. I've seen many folks invest in equipment with less capability only to leave the hobby because of less than stellar results (see what I did there ).
If you're planning to stick with an Astrotrac, I'd recommend sticking with shorter focal lengths to start. I know Fred has used his 500mm howitzer on an Astrotrac. But the chances of success will be much higher starting with wider views vs. starting at long focal lengths. With an EQ mount, 500mm is a great starting focal length. But for something like an astrotrac, I'd start much wider, as your success rate will be much higher. Using your lens at 100mm would be a great place to start.
Generally wider focal lengths don't require highly accurate tracking and is more forgiving to polar alignment. But as you increase the focal length, both of these become more demanding.
If you're interested in shooting galaxies you'll need a much longer focal length (more than 1000mm is better). Most (except Andromeda) are tiny. At my 530mm focal length, most are mere specs in my frame. Conversely, shooting nebula (my passion) is much easier at wider focal lengths. Most cover large areas of the sky. In fact, an area like Cygnus has huge swaths of nebulosity. A focal length of 100mm would be great.
If you're interest is nebula, you might need to consider something else. The vast majority of nebula emit light caused from the ionization of Hydrogen (and other gasses). Hydrogen is the brightest and most common. This light is deep red (656.28 nm) and is far enough into the red that the stock UV/IR cut filter(s) block most of this color. Some cameras have more sensitivity to this than others. But generally you'll have much better results on nebula with a modified camera. Depending on preference, the UV-IR filter can be replaced with one that passes the hydrogen emission. But many choose to have a dedicated astro camera and have a full-spectrum modification, which pass all the wavelengths to which the camera is sensitive. This is a big topic in itself...
As an example take a look at these. This is an RGB shot, similar to what a DSLR would see:
And this is the same area shot in RGB, with the addition of Hydrogen (called Hydrogen Alpha ) added:
As a review:
Nebula -better with shorter focal length telephoto lenses, may need a modified camera, lower guiding accuracy requirements, more allowable error on polar alignment
Galaxies - Most need very long focal lengths, could be better with a crop-sensor camera, requires more accurate guiding, requiresmore accurate polar alignment, can use stock camera.
Hope this helps...