Actually, no, not many of them do have a free trial or lite version unfortunately. There are lots of free pdf apps though, so be sure to look through the app store at some or try a few - if they meet your needs no point paying for one of the other apps.
If I had to pick one office app, I think it would be QuickOffice Pro, but it is really close between it and Docs to Go as both are very well done apps and work quite well, but I think QuickOffice is now a bit more polished than Docs to Go, at least the iPad HD version.
For PDFs again it is hard to say - you should probably read some of the online reviews as the apps I mentioned have been around awhile, so there are lots of reviews and actual user feedback on many iOS/iApp forums.
I do use GoodReader the most I'd say, but it was also the very first pdf app I bought (I just recently bought iAnnotate since I'd read enough about it to think I should give it a try). Most of these apps have a bit of a learning curve to really take advantage of their features, so be prepared to take a little time with any one of them to really get proficient in using them.
My use for pdfs is mainly in literature I need to read for work (scientific journal articles) and I make my notes directly in the pdf files. However, I am not creating my own pdf files very often at all, just marking up downloaded ones. That may be a factor in your choice as well.
I also do not make notes in pdf - I use two main note apps, Noteshelf and Beesy. For general notes (hand written and/or typed) there are two newish free ones worth looking at - Notes Anytime, and Remarks (by Readdle). Notes anytime at first glance might appear like just a bit of a fun sketching app, but really, it is a very nice notebook app with free hand drawing and writing, plus keyboard input, with folder organization and so forth. I suspect it will not remain free forever.