Internal links are incredibly important in your SEO efforts and all you have to remember is to make them descriptive. So no 'click here' links and the like. If the link leads to a page about red widgets then the link should be 'red widgets'.
As search engines cannot see graphics, and they are highly suspicous of alt tags, using an image is a route that should generally be avoided if the text would be useful.
This does not mean your website is going to have to look dry and dull. There are ways of creating text links that look like graphics and so are appealing to the reader and readable by the search engines.
Let's take this example:
It looks like a graphic because we have put a graphic behind the text but it is actually text, and it is text which means something - 'How to SEO' ... so everybody's happy.
If in doubt open Google Webmaster Tools and use the 'Fetch as GoogleBot' feature to check if Google can see what you can.
You should also bear this in mind for links to social networking websites. You may want to say 'Join us on Facebook' or 'Follow us on Twitter' but this results in the search engines starting to believe that some of your keywords are 'join','follow' and 'us' because they appear in a link on every page. To avoid this always make such links graphics. This is exactly a time when you don't want a link to be powerful in the eyes of a spider bot crawling your page.
Bear in mind that most search engines stop following or indexing links after they have reached the 100th one. So if you have something important to say in your link keep it near the top. If your page is large and does contain over 100 links assume most of what is near the bottom is going to be largely ignored which means:
I'm Tim Hill, a Search Engine Optimisation and Online Marketing specialist. I created this site to help others understand that SEO is not a mysterious black art!.
If your a newbie try the Getting Started in SEO page, otherwise feel free to dig around and learn more.