Forget the UV filter. It does nothing except to maybe ruin some otherwise good shots. Think about it..... the lens is carefully ground glass and you pay for that. Your UV filter is a cheap piece of glass not ground nearly as well as the glass in your lens.
A circular polarizing filter is nice to have. It will help block out glare on sunny days and also help bring out the details in clouds.
The use of filters is a very personal choice, some will swear by them, others detest them.
Bob - with reference to your post regarding cheap not as nicely grounded glass... Isn't a circular polarising filter the same thing - a cheap not so nearly nicely grounded piece of glass?!!!
Yes you will get what you pay for.
I personally see no difference when there is one on and when there isn't, therefore I use one to protect my lenses all the time (I have 2 kids who like to touch the glass, or knock the camera occasionally!
To that end, I pay a little extra and go for a decent respectable brand - Hoya, and more specifically their Pro-1 Digital series.
Get a spare battery if you can or need it - I've managed a few hundred shots in a single day with and without using the onboard flash, and the battery has just about reached 50% mark.
Lenses has been covered already, but I'll put my vote to the 35mm and 50mm f/1.8G lenses too - I have the later and it is an amazing lens (though you may find it a little too close when indoors). Set your 'kit' 18-55mm to 35mm and then 50mm and see the difference, it will help you decide towards one or the other.
Do you need zoom? Consider the 55-200mm or the 55-300mm (depending how far you need to reach). Most people on here will suggest the 55-300mm as it gives you that extra reach, but if you don't really need it, then don't get it. I have the 55-200 and rarely go over the 150mm mark so am quite happy with my choice.
A bag for your gear? Have a look at the LowePro flipside range (I noticed you said the slingshot only has one strap so assume you want two).
Oh and most importantly if you haven't already - a good SD card.
Sandisk Ultra or Extreme are good ones - both class 10 cards, and more importantly for your D5100, both are UHS-1 compatible cards
16GB is probably plenty depending on how much you shoot, what settings, and how often you backup those images off the camera/card.
Hope that's enough to keep you buying for the while, anything else, please let us know