I've been shooting with the D5100 for a while now. In fact, most of the pictures in my gallery are with the D5100 now. EXIF data is included with all my pictures so you'll know what's what.

I agree with Gamekiller48 about the 35mm F/1.8 and think any D5100 without this lens (or the F/1.4 version) is missing out.

Couple things I've like to mention about the D5100 though which you should know about if you don't already.

1. It is a DX body (Crop) with a factor of 1.5x . What this means is that the equivalent focal length of anything you attach to it will be X1.5. For example, the 55-300 that you mentioned would actually be the equivalent of an 82.5-450mm and the 35mm that was suggested would be ~52.5mm.
2. When using the self timer (like "Wait five seconds, then take the shot"), you have to turn the self timer back on after every shot. At first this sounds annoying and it will be for a bit but in situations where you would use it, I'm generally taking my sweet time to get things right anyways so it's not that much of a bother. Using the quiet shutter (You press the shutter, the camera flips the mirror up, waits, then opens and closes the shutter) will usually remove any shake from hitting the shutter button and will not require you to change anything between shots.
3. It's worth mentioning that the HDR function is nice but only works when shooting in JPEG format and not RAW. The camera also has a feature called Active D-Lighting which is similar and -does- work when shooting RAW. Active D-Lighting can be nice sometimes because it brings out the shadows while not effecting the highlights. There are several different settings for this which increased the amount of ADL being applied. I haven't done much testing as to whether or not it's better to keep it off and fix the shadows in post with the RAW file but you can decide for yourself when you are playing around with it. I use it sometimes but not extensively.
4.a You'll find that there are lenses labled with "DX" which means that they are designed specifically to work on DX bodies (remember number 1?). This also means that they will not work very well on a full frame body. It's a good idea to invest in lenses that will function on both kinds of bodies in the event that you either a)upgrade your camera somewhere down the line to a full frame body or b) wish to sell the lens off for whatever reason. Being able to sell to both DX camera owners and full frame camera owners puts you at an advantage there as well since the resale value of lenses that were taken care of is excellent. An additional point in favor of non DX lenses (sometimes referred to as FX) is that on a DX body they will only use section of the lens, particularly they end up using the best part. The edges of lenses tend to get less sharp and have color fringing. This is less of an issue on a DX body.
4.b In this regard, you may find that instead of the 55-300mm DX lens, the 70-300 FX lens is a better investment. Also, don't be afraid to buy lenses used. You can save a lot of money buying used lenses and from personal experience, I've never had a bad experience buying used. In fact all of the bird photos except the Quail in my gallery (taken with a different used lens) were taken with a 70-300mm F/4.5-5.6 that I bought off a guy from craigslist for $200 less than retail.

Whatever lenses you decide on, the important thing is that you enjoy them and if you're happy with whatever purchase you make, then that's all that matters. The D5100 is a wonderful camera and I've enjoyed shooting with it every time I bring it out.

I also have a D5100 and didn't regret spending that amount of money on it. I went for the 18-105mm Nikkor, so I can't tell you anything about the 55-300mm lens.
Some things you might already know about the camera that are worth mentioning anyway:
The Nikon5100 has a software intervallometer included - you can programm it to take a picture (for example) every ten seconds. This intervallometer works good, but there are some limitations:
1. You can only take 999 pictures in a row. After that you have to restart the intervallometer manually (this limits the amount of time you can cover if you want to make a timelapse-movie)
2. You can't use the built-in HDR-function with an intervallometer (software or hardware): After one HDR image the camera switches back to the normal photography mode automatically
3. It doesn't work in Automatic-Mode

I would also like to say some things about the video function (even if it looks like you only want to take pictures):
There are some different quality settings for the videos like '1080p High Quality', '1080p Normal Quality', '1080p Low Quality' (and also 720p High, Normal and Low).
If your SD-cards can't write the information fast enough you won't be able to record videos in 1080p High Quality for longer than 30 seconds. There's also a limitation so that you can only record 20 minutes maximum (that's because Nikon would have to classify the camera as camcorder instead and then they would have to charge additional taxes or something like that)

A UV-filter or something like this to protect the lens from scratches is a good investment. You should also think if you want to buy an insurance for the camera (I did so, 50€ for 1 year insurance that covers theft, scratches on the lens (even self-imposed ones), and all other damages that could happen to the camera).

It's my first camera so I can't provide you awesome examples what is possible to achive with this camera, but here are some of my shots:
[link] (I think this is the size of your images, the others I posted are either downscaled or panoramas)
[link]
[link]
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If you have anymore questions feel free to ask.

I have the D5100 and I love it. Im not the best photographer but in more capable hands it can be an amazing tool. heres some pics Ive taken [link]

to be completely honest a good lens to have is the 35 1.8. It has a great maximum aperture For low light Situations and you can get some fantastic shallow depth of field. though the bokeh isn't as creamy as the 50mm 1.8 or 1.4 its a sharp lens that you wont regret buying. 55-300 mm only has 3.5-5.6 range of maximum aperture so its not as great for low light and though its a good lens(I have the 55-200) starting out with a fixed lens with a dslr can help you really see the artistic capabilities.
the only caution I can really give you is after using it a while you kinda get the itch for a more capable DslR. If you can afford it I'd go with the D7000 but if not this is more than capable.