If you are limited in how long you can expose for, then I recommend using a higher ISO, such as ISO 1600 maybe even 3200, use short exposures of around 30 seconds, and get many of them. I would say get at least 16x, however 25x or 36x would be better.
The reason you want to use a high ISO is the higher the ISO, the lower the read noise in most cases. The reason you want to get many frames is you can stack multiple frames together after "registering" them (which aligns each one on the stars). By stacking 16 frames, you reduce noise by SQRT(16), or 4x. By stacking 25 frames you reduce noise by SQRT(25), or 5x. By stacking 36 frames you reduce noise by SQRT(36), or 6x. You could stack 64 frames to reduce noise by 8x, but without tracking that is likely to result in funky star trailing in the corners (you'll get a little of that with 36 frames even, but it will be small enough that you could crop it out.)
You can register and stack the frames with a free tool called DSS (Deep Sky Stacker). DSS will take all the frames, align them with each other, then stack them together to average out the noise. Stacking like this is called "integrating the exposure". This should get you a decent result using very short exposures, even without tracking. Once you have a stack, you will usually need to "stretch" it to reveal fainter details, enhance contrast, etc. Think of this as basically the same as pushing shadows with a high DR scene.
If you want to get better results with much longer integration times, you could look into getting a small tracker. A tracker is a simple astrophotography mount capable of holding a DSLR and a small lens, maybe up to 135-200mm in length. They will usually track the sky for up to 2 hours, which is usually more than enough to get lots and lots of frames to stack for a very clean result.