I'm very burdened thinking of the two lenses the nikkor 16-85 and 70-300 lenses?

What do you guys sgest me to buy first? And why?

If this your first to buy lens then I suggest you bought the one that suits your interest and most importantly to your budget. As for me, I preferred to buy the Nikkor 70-300.

These two lenses are like north and south poles.
16-85 mm can be treated as a good walk around lens and leave it on the camera.
70-300 mm would be your special purpose lens when you travel or you wish to capture object at long distance.

There's a 15mm focal length overlap between these two lenses.
So I'd advise you to go for a regular walkaround lens first and then invest on a telephoto lens at a later point of time.

If you buy the 70-300 mm lens as a first lens, I'm sure you would have a lot of trouble while shooting a function in small
to medium sized room. You will end up buying another lens almost immediately to compensate for the portraits/party pics.

18 months ago, I have purchased this lens (after 2 months of research). I never had a moment to regret. I'm not a pro.
Also I'm not expecting any extraordinary sharp pics that comes with the Nikon 24-70mm category lens.

In my opinion this lens is a keeper for atleast 5 years for any DX user before going for the next high end lens.

What you get from 16-85mm lens when you fix it on a DX DSLR:
1. The lens would become a 24-127.5 mm lens (with the 1.5x Nikon cropping factor)
2. You can have a decent wide angle coverage
3. You can have entry level telephoto range that is not bad
4. 16-85 also has a metallic mount and is better than many of the kit lenses
5. Reviews say that this lens has a decent result when operating at 16 mm
6.It may not be as good as a prime lens, but you can have a decent low light photography

As per the www.thomhogan.com reviews also it's one of the costly regular walkaround lens made by Nikon for DX users.

Once you feel that you have a regular necessity to shoot beyond 127.5 mm lens then you can get the other lens.

Well you're the one who should know the most, these are two different ranges. You want something for things far away like sports, zoo, animals outside, or something all around with more zoom than 18-55mm. Knowing what you currently have would also be good, if there's not kit lens then 16-85mm would be better.

Here's a Lens Buying Guide - http://www.the-dslr-photographer.com/2009/11/buying-a-lens/