For a specific example, I got the idea from reading about the death of Conan II of Brittany, who was likely poisoned by William the Conqueror. What poison would William have sought for this purpose? Were there higher and lower "tiers" of poison that were more or less effective, and would their value have been directly connected to their toxicity?
I've really only studied the situation in the high Middle Ages and early modern period, but at that time there were essentially a couple of major alternatives available: arsenic-based poisons, and what was known as "corrosive sublimate" – mercuric chloride.
The problem that poisoners faced, then as now, was not so much finding a poison that worked (although understanding exactly what it was about a poison that caused it to work was, of course, pretty sketchy at the time, which is why the basic ingredients we know were active poisons were so often supplemented by others that were less toxic, or even not toxic at all, such as toadflax, Spanish Fly, extract of snapdragon, a solution of pennywort known as aqua cymbelaria, and even madmen’s spittle). It was finding a poison that was sufficiently subtle in its actions to not make it immediately obvious that the victim had been poisoned. In the period you're interested in, that problem was lessened by the ubiquity of sudden and painful death from all manner of ailments, even in people who had previously been young and healthy. For that reason, while poisoning was often suspected as a cause of death, it was almost always very difficult to prove that it had been involved.
Working back from the symptoms reported in major cases of poisoning, such as those committed at the Medici court or, later, the cases that breathed life into the infamous Affair of the Poisons at the court of Louis XIV, we can say with some certainty that the majority apparently involved various arsenic-based compounds. But during this same period, a belief evolved in the existence of – actually non-existent – so-called "slow poisons", which, it was believed, were far more precise and had essentially no tell-tale symptoms. This belief, in turn, fuelled quite a lot of work in alchemical laboratories, and eventually some interesting 17th century poisoning scares.
I wrote in some detail about the slow poison called "Aqua Tofana" here, and also contributed to a book of essays on poison in the period you're interested in, Toxicology in the Middle Ages and Renaissance (2017). The latter book includes several other pieces that you would find of interest, including Sheila Barker on poisons at the Medici court and Cathy Cobb on the Borgias. Jo Hedesan's chapter on alchemical perspectives on poisons is excellent for filling in detail as to what contemporary theory had to say about how they worked.
I'd also strongly recommend that you take a look at u/sunagainstgold's fascinating look at medieval cases of supposed well-poisoning for an alternative perspective on the whole issue.