Need Sub Woofer Help!, Replacing woofer with new one that doesnt use the mount. Options

[BNRWN]

hey all. Im newto the site but joined for a purpose. So im driving an '01 Avalon and im having, of course, problems with the woofer. It had been blown/ripped for quite some time until i decided to try to fix it with some adhesive. It actually worked but after awhile its starting to rip again, which i can tell by the sound hah. Im pretty fed up with this little menace and i've decided im going to go with a different approach and by a new subwoofer, and use the adapter from the stock one to connect it to my car.

Now, there's a few things i've found out about doing this, but I'm not so sure about it seeing im pretty new to the sub woofer area. Firstly, will this even work? i cant imagine it wouldn't, though I'm a little confused on what sub woofer i would be able to buy seeing the 8" stock one is pretty wimpy. I'm not looking for anything major i just want a small (looking at about 10") sub for a little extra bass when playing my music. Does the wattage/OHM matter?

Ive also removed the 8" woofer and have tried to remove the adapter thing from it but can't exactly figure it out/get it disconnected. Does anyone have experience with this that can sort of give me the way to do it?

Also, if anyone has some suggestions for what sub or subs i should be looking at can give them to me that would be great! :p

Please help! getting frustrated lol!
Thanks!!