VHS Camcorder but with SD Card instead?

Put the effects on afterwards in editing (in 'post' [postproduction]).

When adding effects always work on a copy file!

I have an old top of the range Panasonic mini DV(tapes) camcorder which cost me 2.5g 5 years ago. The tapes are expensive and it has been playing up with some brands of tapes. I dusted it off and was experimenting with it when I discovered it has an SDcard slot.

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Use modern equipment, shoot the best quality footage you can and then apply effects in post.  A lot of video editors have vintage effects built in and there are loads of plugins available for adding noise etc.

save your digital video in MPEG1 format, that should give you a pseudo VHS look.

There are filters you can use to give the VHS look.

If you just want the effect, rather than the actual camera, you could resize the video to eg. 640x480 then resize again up to whatever you want the actual display size to be - if you even need to.

If that does not give a fuzzy enough effect you could go even lower - 400x300 or 320x200; some very early digital video cameras used that resolution.

720x480 would be approximately "DVD" quality, to put it in context.