Nikon D3100 lens compatibility from other brands?

I have a NIkon D3100 camera and I'm looking for new lenses. I only have an 18-55mm (AF-S DX NIKKOR 18-55mm f/3.5-5.6G VR lens) and I'm looking for something up to 200 mm. Preferably beginning with 55mm. I'm no expert as I'm only a beginner and I'm beginning to love this hobby. My question is how do I choose a compatible lens for my DSLR? I'm not set on staying with Nikon's Nikkor lenses as I do not want to be restricted to choose if I can actually look for other brand lenses. I'm not looking for Nikkor lenses compatible with my camera. Is there some red flag I should look out for If i buy other brand lenses? I'm also looking for a lens/lenses that is not muy caro (expensive). Thank you very much, your help is appreciated

Added (1). Also, I prefer manual focus

When you say that you prefer manual focus, does that come from the experience of turning off the AF on your 18-55mm and finding that you like it better that way?

Hello just in case you need new camera www.belowprice.org have a few to choose from.

My advice would be to stick to Nikon lenses.
You know they will be fully compatible and will last a lifetime.

Manual focus Nikon AI and AIS-fit lenses won't allow metering on your camera.

Third-party lenses from Sigma, Tamron and Tokina will fit - if you specify Nikon mount - but lenses without motors won't allow autofocus on your camera.

Lenses made by Pentax, Sony, Canon, etc. Won't fit.

First, make sure the lens has a Nikon mount. Next, make sure it has a built-in autofocus motor. Limit yourself to the following brands and specs.

Tokina IF or IRF
Sigma HSM or IF
Tamron USD or IF

Among the three, Tokina is the best brand. Don't consider others unless of course it's Nikon. Here's a link to your current model choices.

http://www.bhphotovideo.com/...rtclk=sort

I have included some lenses that start at 70mm and 80mm. Don't worry. You won't miss the 55-70mm or 55-80mm gap. It's just a step or two backwards anyways.

Lastly, you should also be concerned with the anti-shake technology. Nikon calls it Vibration Reduction (VR), Tamron has Vibration Compensation (VC), Sigma has Optical Stabilizer (OS), while Tokina labels it VCM.

This camera supports autofocus with AF-S and AF-I CPU lenses only. AF-S lenses have names beginning with AF-S, AF-I lenses names beginning with AF-I. Autofocus is not supported with other autofocus (AF) lenses.