Welcome to the forums Japie, you've picked the best way to start, using a DSLR and tripod.
With a $500 budget I would personally suggest spending that on getting a mount for your DSLR and using whatever lens you have. Being on a tripod you are limited in exposure time, with an equatorial mount you can have a LOT of fun imaging the sky with longer frames.
Although I have never personally used one, I have heard a lot of good things about this product.
https://binocularandtelescope.com.au...er-bundle-red/
It is a very portable EQ mount designed around DSLR astrophotography. All you need for it is a stable tripod and you're ready to go!