I don't think the "Insert Image" icon ("mountains and sun" above, or what is supposed to look like a postcard) was an option on the earlier version of this forum software. That is another option for posting pics.
Usually Photobucket will resize the images to postable sizes when you upload them. Could be a setting there you can change.
But if you click on the IMG link to your picture on Photobucket (where it briefly flashes "Copied"), you don't need to use the postcard icon at all. You may then paste (position cursor where you want the picture to appear, then hold "Ctrl" key and press "V" key) that image anywhere in your reply box, using Quick Reply or not.
Remember to add a space (hit "Enter" key) between the links to the pictures or they will appear butted up against one another, which can be confusing to see where one picture ends and the next begins. By add a space, I mean like this:
Here is one picture link code
Here is the next picture link code without a space.
Here is another picture link code
Here is the next picture link code with the space.
So there will be a gap between the two in the latter posting.
Photobucket keeps changing the layout of their web page. I have updated this sticky about 4 times over the past years, but I have given up on doing that. For one thing, there is now the postcard icon one can use to post pictures (though I really don't think that's any easier) and for another, the key principles in this sticky remain the same even though the appearance of the Photobucket (or ImageShack or whatever) may have changed.
As always, post for help if you need it!