We sequenced plant DNA samples using ITS, 5.8s and rbcl primers and we were planning on performing a phylogenetic analysis but I wanted to know what other possible information could be inferred from these sequences.
There are a lot of literature on this question exist. In general, in phylogeny rbcL used for separation gerera and sometimes another taxonomical categories and for detecting prarents (in most cases rbcL is maternal-inherited). This gene have no crossingover and polycopy. ITS more variable than rbcL, but have secondary structure which are more conservative than sequence.
At first I wish you fing and read main articles and observetions on this question. Great work on describind principles of work with such sequences was provided by Annette Coleman, Mark Chase, Mattias Wolf, Pamela Soltis, Douglas Soltis and manyother researches
There are some links on some of such publications (this list is far not full, but can help you to start):
Please, specify the type of organism you want to use in phylogenetic analyses!
In most cases, 16S or 18S and ITS will provide good information for species identification.
Sequencing "ITS only" may be sufficient for species identification, because higly variable, but this depend on the database you have on your organism. It may be not sufficient, and it is sometimes hard to align your ITS with others (you need to delete highly variable regions). Also, you will need to perform secondary structure to identify variable parts (you may use a website such as mfold).
If you want more resolution (for example, to show differences within close or same species), longer sequences or other markers should be considered.
You can also use concatenated dataset of 18S+ITS1+5.S+ITS2, but it will require more experiments and phylogenetic analyses :) I did it for Chlorella -a green alga- organisms (see my paper).
As proposed above, the best way is to find the phylogenetic paper on your organism!