Designers can design in different color spaces, the most common being CMYK and RGB.
CMYK is what your printer will need and RGB is what your web designer will need. If your logo will be used exclusively on the internet you will only need RGB. The EPS vector file given to you is always in one color space and higher quality design programs can save to the other color space effectively.
Both color spaces can save into each other but there can be problems. Each color space has limitations. Most Designers know the limitations and easily work with them.
Many experienced Designers use the Pantone® matching system to make designs because there are set RGB and CMYK values that do not change. If you have preferred colors, it is often good to request Designers make their designs using this system. you can also research them on Pantone's website.
Super bright RGB colors tend to translate into much darker versions when printed in CMYK. To avoid disappointment, you can ask the Designer if the colors will be the same. Asking them to design using the Pantone® matching system will avoid such problems.
To help Designers give you their best, it is a good idea to research font types you like on popular sites.
There are basically three kinds of fonts, Freeware, Donationware and Payware.
Most Freeware fonts are 100% commercially usable without cost or limitation. Some such fonts may simply be personal projects of artists that may use proprietary fonts from another business, but this is very rare and usually not an issue.
Donationware fonts are generally more similar to Payware.
Payware fonts are just that, fonts you pay for. These include some of the most popular fonts designed. Some are quite inexpensive, some are not. That will rarely be a problem for you since Designers must make their winning entry converted to curves and they are expected to have purchased the rights to use the font to make designs.
Designers should never send you fonts that are copyright restricted. They can send you the link to the fonts they used, or it the font is Freeware, you can be sent the entire ZIP of the font as directed by the font designer.
Please note that all final files are sent as vector images, not with fonts embedded. This is known as "reducing the image to curves."