Having read a synopsis or two, I'm wondering how to get into this universe, and thus what the suggested order is.
Given the various authors involved and the somewhat convoluted nature of the source material, there doesn't seem to be any authorised reading order, however serious fans seem to split evenly on two schools of thought on the subject;
A pure in-universe chronological order is one of the options. There are no major spoilers caused by following this technique, but it's quite heavy-going to begin with and you should be aware some of the truly major works in the canon (notably The Mote in God's Eye and The Gripping Hand) don't turn up until much much further on, after you've ploughed through several dozen lesser works and obscure short stories.
Your alternative is published order. This seems to make more sense in terms of getting to grips with the universe and the worldbuilding that goes with it but you may find that the later works can become somewhat repetitive and divert quite strongly in style from the earlier books, simply because they were written much later, during which time the author's voices matured and changed.