I need to use it for a web site, as a watermark on digital photograph as well for printing on photos, business cards, etc.
Ideally you tell your designer your intended uses and requirements and they will tell you what formats you need, and what to use each for.
CMYK & RGB
You will need both CMYK and RGB versions of your logo. Generally, you should use CMYK vector files for print and RGB files for screen (i.e web). A lot of photographers do however print their photos in RGB so you should use an RGB logo as a watermark if you are doing that.
Vector & Raster
You should have both vector and raster versions of your logo. Raster images are made up of pixels, like your photographs. They have a set size and can't be made bigger without losing quality. Vector images on the other hand are made out of mathematical paths and points, they can theoretically be resized to any size you need.
An example of formats I normally supply:
- JPG (RGB / Raster / high res & low res)
- PNG (RGB with transparency / Raster / high res & low res)
- SVG (RGB / Vector)
- PDF - (CMYK / Vector)
- EPS - (CMYK / Vector)
- AI - (CMYK / Vector)
A few notes on the different formats: Most vector formats can contain raster images too so don't automatically assume your PDF is a vector, check with your designer. For raster versions of your logo, PNG is generally preferable over JPG. PNG is a lossless format which means you don't lose image quality as you do with JPG. PNG has full alpha transparency too so that you can place it over other images (as a watermark over your photographs or over a background on your website for example).
You can read more about what different image formats to use here:
Ideally, your designer should supply you with all the different formats you require, with appropriate filenames (including size, cmyk/rgb etc) in a logical folder structure. That could be a folder for each format, a folder for print and web, a folder for each version of the logo—it doesn't really matter, as long as it's easily accessible.
Should it be easy for them to provide all formats requested.
Yes, it should. Not all designers are equal though. Your designer should have created your logo as a vector, which would make exporting to different sizes and formats no problem at all. Some will create a logo as a raster image though (they shouldn't), which would make it a lot harder.