Practically everything - that means more than one lens.

A superzoom, ~18-200+mm can be very convienient and fine for hand holding in good light levels, or if you can shoot long exposures. However it will be much to slow (optically) for shooting hand held in low light and possibly to slow (mechanically) to aquire and track fast moving objects.
I do own a Tamron 18-250 and it is an OK lens (not great) and I mostly use it when I have to travel real light, in he daytime, and I want to have a lot of versatility over a reasonable focal length range, in a relatively small package.

You may want to think more than one lens (you do not have to buy them all at once). From personal experience if you buy better lenses stright up (I didn't always) you will save money in the long run.

In good light or shooting long exposures an F4 will be OK
For an ultrawide I use a Tokina 12-24 F4 - It is an OK lens however nowdays there are better choices available.
For a mid range tele I use a Canon 70-200 F4 L (it is a great lens)
For a long tele (birds and motor racing) I have used a Canon 100-400 f4.5-f5.6 IS L (it is a a great lens), but nowdays use a Sigma 150-500 which is just an OK lens.

If you want to shoot hand held in relatively low light think fast lenses, at least f2.8. Fast zooms can get very expensive very quicky. I do own Tamron 17-50, however it is a great lens as it does have difficulty in aquiring focus in low light.
See my previous reply in this thread for some other suggestions.

The Tamron is a good lens and they actually make 4 lenses of this type with the newest being a 16-300. It gets pretty good ratings and is $629 from B&H or Walmart.

Sigma has 18-250mm F3.5-6.3 DC (OS)* MACRO HSM that has just been reduced $200 because a new lens in the catagory has just come out. It got very good reviews when it came out in 2012. It is now about $325-350. That would leave you half of your $700 limit towards another lens. An ultrawide or macro dependent on your interests.

Hello from The Shire and Welcome to the Hog! I think you will find this place very helpful and enjoyable. 
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Frodobaggins