Where To Start When Collecting Roman Emperor Coins

As in collecting every type of 'thing' your budget will limit you. Unless you have very deep pockets some emperors will be almost impossible to acquire. Some lasted but a few weeks or even a few days. You need decide first what you might be able to afford. The first century emperors (Augustus through Trajan) tend to be the most well known and can command some serious money. Although a nice silver denarius of Trajan can usually be had for under $40. Some of the real 'skunks' (Caligula and Nero) can be several hundred or thousands for a similar condition coin. 'Nice guys' with longer reigns tend to be much cheaper. The third century was a very chaotic period with very many emperors (often more than 4 at the same time !. The coins tend to be less impressive overall but can be acquired often for under $20 ea. excepting those short lived fellows. If you like ancients you really should read up on the times. It can get very complicated and take some time. But by learning the backround first you will enjoy your first purchase all the more. Perhaps a few bronze coins from the time of Constantine would be the best affordable way to start. These can usually be had for modest amounts. The inflation of this period was terrible and the mints were working overtime to keep up with demand. The coins tend to be small and the artistic style may not be the best. But they are plentiful and lower grade bronzes can be had for a few dollars apiece.

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FR summed it up well, so thee really isn't anything else I can add other than what ever period you decide to collect come visit us often. You can learn a lot here. Also check out the sticky section on Books, downloads and websites. There are books on ancient coins you can download along with tons of other information.

I would only add that buying uncleaned lots can potentially be a disappointment. Unless you have a keen eye for those lots with more possible winners than others you might spend a few dollars apiece and end up with a small pile of 'junk'. Anyone selling these lots usually looks them over and pulls out the ones that may seem like 'winners' leaving those with less appeal. Nice Constantine period bronzes can be found for around $10 or even less if you have the patience. People overpay when they tire of searching and do something "hasty". I have done it and so have we all ! The idea is to keep the mistakes to a minimum. If you check ebay you will find plenty of coins of Constantine and his family (Crispus, Constans, Constantine II, and Constantius II ...... as well as some other 'folks' ie Constantius Gallus and Julian II).
If you check your local Library you should be able to find a book with 'bio's' of Roman Emperors. An easier course would be to simply go to Wikipedia and look up Constantine ! His biography will give you links to all the major characters of the period. It can get a bit confusing especially with so many people running around with names that are all variants of the name Constantius (father of Constantine and a "Generallissimo" emperor himself) ! Constantine the Great was not only to become a future Christian 'saint' but was the eldest son of the Emperor Constantius who himself was deified (by the pagan Senate) upon his own demise so the name was no doubt considered 'illustrious' if not completely confusing for the novice.
You mentioned your grandfathers collection so I assume two things. First you are probably not 'grey' haired and second that you have a family member who "collects" and so should be able to point you to a dealer somewhere in your vicinity. I assume grandpa doesn't simply collect coins he finds in his spare change. Some reputable dealers like to tempt younger people into the field of collecting. If they are smart that is ! Once you become 'hooked' on coins they know they can usually make you a regular and thus relieve you of that extra money that so pains you to have inside your pocket !

Beware ! Collecting ancient coins can become highly addictive with secondary effects like changes in mood and behavior and anti social tendencies like traveling long distances to go to "Shows" and losing yourself for an entire day looking through entire inventories of coins.

Or you might have tons of fun ! It is hard to say ........