Hello and welcome.

Things that make a coin valuable:
- Precious metal content. Gold and silver coins are usually more valuable than base-metal coins.
- Rarity. This is a combination of mintage (how many were originally made) and survival rate (how many are likely to have been destroyed since then).
- Condition. Generally, better condition (less well worn) coins are much more valuable than otherwise identical worn coins.
- Demand. A coin might be really, really rare, but if no-one wants it, it won't be valuable. Some coins are simply more popular than others.
Another factor in the price discrepancies you are seeing is that there is a great difference between what people are asking for a coin, and what people actually get for a coin. Some sellers, either through ignorance or malice, offer completely unrealistic prices on their coins.
There are coin catalogues that give typical selling prices for most coins; an honest, reputable coin seller will not aim to go much higher than the prices listed in those books. You're in Britain; the standard coin catalogues people seem to use there are the Spink catalogue (which covers all of British/English history) and the Rotographic guidebook (which only has modern coins, 1813 onwards).
For foreign/world coins, the American-made Krause catalogues are the standard reference. There is an online version of the Krause catalogue maintained by NGC, one of the American coin grading companies; you can find it
here. If you know the country, date and denomination of your coin, you can look up the price guide there.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis