You might want to start with the history, so you get an idea of which period interests you. Some emperors were more interesting than others and that doesn't necessarily correspond with how many coins they issued or the cost of those coins.
The coins, however, fall into distinct categories, which have fairly clear characteristics (and different price points). They are very often sold according to those categories, so it helps to understand what these are.
Roman Republican (509-27BC)
The important distinction here is that this is pre-Augustus and the creation of the role of Emperor. Rome was run by Consuls - two per year - to prevent any individual getting too powerful (as in the monarchy it replaced). So you don't get busts of rulers on coins - although plenty of gods. Coins were produced in Rome for use in Rome.
Roman Imperatorial (59-27BC)
A subset of Republican, during the Imperatorial Triumvirates - when power was taken from the Senate and consolidated with three individuals (Julius Caesar, Pompey, and Crassus). You start to get individual rulers on coins, and these are such people as Caesar, Marc Anthony, Brutus and Cleopatra. Unsurprisingly, these are not cheap.
Roman Imperial (27BC-426AD)
This is the Roman Empire, from Augustus and the creation of the role of Emperor. Coins feature the Emperor and were eventually produced across the Empire for use across the Empire.
In the early part of this period, you get a lot of silver denarii that are often well worn (but not cheap) since hoarding was less common than later on. There are also brass sestertii, which are also well worn but very large and often beautifully engraved.
In the 200s (before the Tetrachy) a lot of cheap, poor quality coins were made with lower silver content. (At least, we find a lot of them, because these were troubled times and hoarding was at its peak). This period also saw a large number of 'barbarous imitations', mostly of Tetricus I or II. Although these are counterfeits, they are easily distinguished, as they are usually very crude. They weren't meant to trick anyone, rather there was a shortage of coins at the furthest reaches of the Empire and people needed to use
something. They are also very cheap.
Roman Provincial (44BC-293AD)
I see this mostly as a subset of Imperial, although it could cover coins going back to 241BC. As the empire grew, it became necessary to decentralise and create administrative regions outside Rome. Similarly, coins began to be produced in these regions and not just Rome - places like Sicily, Egypt, Lycia, Crete and Syria. These coins feature Emperors but were mostly used only in the province that minted them (which distinguishes them from Imperial coins).
Tetrarchy (293-324)
A subset of Imperial, after Diocletian divided the empire between four emperors - two senior (Augustus) and two junior (Caesar). One Augustus and Caesar pair covered the West, the other pairing covered the East. All four appear on coins produced on both sides of the Empire (which means there are up to four times as many rulers to collect). The quality of coins improved a lot, although now they were mostly bronze and not silver.
Constantinian (307-363)
A subset of Imperial, relating to Constantine I the Great (who ended the Tetrarchy) and his family. They produced a lot of mainly bronze coins that survived in high numbers, making them inexpensive to collect.
The empire then declined, but silver made a return, mostly in the form of the siliqua. These are not cheap and often broken or heavily clipped - the Saxons used them alongside their sceattas, and cut them down to the same size (using the excess to make more coins).
Byzantine (395-1453)
After the fall of the Western Roman Empire, the Roman Empire continued in the East as the Byzantine Empire all the way into the 1400s. Those coins are heavy on Christian symbolism. They're often cheaper than earlier Roman coins, particularly the gold issues.
I wouldn't buy anything off
ebay or
Etsy until you know what you're looking at. Many Roman coins are cheap so you can afford to go somewhere reputable, such as many of the dealers on VCoins. I would also avoid coins with 'sand patina' because this is often faked to hide damage.
Bear in mind, however, that when I say 'cheap', I mean around $30 and up. You can get some really nice late Roman bronzes (Constantinian) for $50 or so.