The installed size of app varies a lot. So there is no one answer. In the App store the size of an app is specified. However, that is the compressed size and it is larger when expanded and installed. Movies can take a GB or two.. You might want to consider getting a 32 GB model since you can't expand the storage. The 8GB version only has 6.4 GB available for the user.
Most likely as many as your want, unless you download apps with tons of data, such as a mapping application, or a app that include lots of built-in images, or its own built-in video.
Otherwise you can most likely have all the apps you want.
My iPod touch is using 5.8GB for apps, and I have 213 apps on my iPod Touch. 80% of them I do not use after downloading them. Of the remaining 20% most are infrequently used, a small handfull are used maybe once or twice a week, and about 7 are used daily.
NOTE: Of the apps I have on my iPod Touch, one is Stanza an eBook reader, and I have 398 ebooks in that app.
However, all bets are off, if you decide later you are going to download any videos, or music (or audio books), or family picture, all of which consume space at a higher rate.