She's 1, she's still getting milk wether breast or bottle. Don't make yourself miserable and don't sweat it. At that point solid meals are still somewhat of a novelty/exploration thing, nothing critical nutritionally.
Serve tinier portions of simpler foods that require little to no prep. Just little things to pick and try from. Bits of fruit and cheese, peas, crackers, etc, so she can grab and play with without you holding the spoon. As long as it's not a choking hazard.
With soups, purees and such, what she doesn't eat, store away in a little container and give again the following day. Don't throw the stuff away after every meal !
See it as shared responsibilities : you're responsible for providing the food, she's responsible for what and how much of it she eats. It really doesn't matter if it's just a bite.
As for the mess and cleaning, you can get one of those plastic bibs with sleeves. I just ran it under the shower after to get the gross bits off and that was good enough for me. My son's nanny was laying a plastic cloth piece on the floor and rinsing it after.
Seriously though, I get how it can be boring and annoying. Best advice I can give you is to not strongarm your child into eating/trying. Let her deal with the actual eating part.