I cannot tell you what to do. I'd be willing to bet my tastes are different than yours. When I do ported boxes, I tune them lower. Currently, everything I do is sealed. However, I did take some time to model some subwoofers I'm familiar with using your box specifications. The Rockford Fosgate did not look as good to me but it would work. Its peak response was at a higher frequency than the others; however, the subs I compared were more expensive.
For a little more than the Punch you can get the Image Dynamics ID10 V.4 D4
The other two were the Dayton Audio RSS265HO-44 and the JL Audio 10W1v3-2 all three of these model fairly well in your box with the Image Dynamics appearing to be a decent bang for the buck choice. I have not heard that model but I have listened to the IDQ model; however, the IDQ doesn't play well in your box.
Regarding safe, yes. Speakers do not pull wattage. The amp gives what you tell it to. The speaker rating is just what it can handle. Unless you plan to just set volume to full when the key is on, you wont even run the 500 watts continuously.
Maybe someone else may know about a budget gem they recommend. I recommend one of the three I linked above.