I have a little collection on my homepage mostly because the first couple indie sites i came across when i first started getting into all this last year also did the same. I'm a fan of little thingies like these: stickers, patches, wallart, pins, etc. My car, water bottle, laptop, work laptop, portfolio, negative enlarger, walls, jackets, bags are all covered in this sort of thing. I love a sticker-bombed look or even a couple simple personal patches on an otherwise plain bag. So, in general I am a fan of it!
BUT I also see that it can easily get out of hand on a website. IRL, the amount of stickers i can put on a thing is limited to space, cost, and general good taste. I've resisted the urge to litter my homepage with gifs because I do actually want my site to feel
somewhat purposeful (it's my portfolio and social landing page). I'm also starting to look into applying a share-alike non-commercial creative commons license to my photography and art, setting up a proper terms of use and registering my art with the copyright office. Reason being I want to start selling my photography and offering commissions.
Not that a big-ass collection of uncredited gifs and graphics is
unprofessional, at least i don't want to be professionally involved with those that would think that. But, like you, i want my site to be a presentation of my own work.
I'm currently redesigning my site to be responsive (flexboxes everywhere), usable on mobile, and accessible for screenreaders and the like. A part of this redesign will likely involve moving that gif collection off the main page, and I'm considering not displaying most of the gifs at all. I'll probably have a page for my "pets" like gyphypet and the like, but random gifs I might not keep around or I might have an archive page.
I
am a big fan of badges that sort of describe something about me or my site (for instance im stealing
this from your page larvapuppy

). Those I'll probably keep around on the homepage somewhere, maybe the sidebar. I try to find sources for most things, or if not then at least link to the thing the badge is referencing (the sublime text badge on my page links to sublime text's website for instance), but I do feel bad just grabbing a random gif that looks obviously like somebody's original work, ya know?