it depends on how many genes or proteins you are looking for. if it is a single gene then a western blot and qPCR ca be used to study the expresssion profiles. if you are looking for large number of genes you can go for microarray analyses. it would be good if u can check GEO (NCBI) and other public databases that contain microarray data. Also, human protein atlas also gives an idea about the expression profile.
You can probably find most of this information already available in the various public databases. People are now using digital gene expression which collates available data sets. This is largely centred on expression at the transcriptome level however there are databases collating protein expression from carefully constructed staining experiments by the likes of Allen Brain atlas and so on. However if you are focused on protein I would tend to do it yourself it tends to be more dependent on the antibody used. If you they used a great antibody, the quality can vary from lot-to-lot.
There have been some great multiplexed methods made available in recent years for both transcriptome and protein (in situ mass-spec).
What kinds of tissues you are looking at and how many targets and how quantitative do you want it to be? I.e. present/absent for inducible genes, or high dynamic range in expression?
These techniques are fairly new so you will have to put the effort into setting them up but I assume a majority of them can be applied to tissue sections you may have already obtained. They are nice as they give single-cell and sub cellular resolution.
If you are only interested in bulk analysis/averages over different cells types from a region of each tissue. You can use standard microarray or proteome analyses.
In terms of accessing already collated data sets you may find this website very useful.