Sites
Casinomeister is one of the top online casino websites. It is sufficiently influential that casinos care what is said about them here. A good site to look at is eCogra, they list over 100 seal holding casinos, and provide links to a number of reputable online gaming portals.
Casinomeister has a smaller list of accredited casinos, however, the standards are likely to be a little higher than eCogra, and reaction times for bad behaviour swifter, and more public.
A good "fun" site is GoneGambling, which offers games where it is possible to win small bonuses for select casinos and bingo halls (between $10 and $50, but a few bigger prizes CAN be won).
888.com is the most "famous" online casino, but one has to be careful of WHY it is so well known. Stop at any Motorway services for a "slash" and you are bound to come across 888.com
They are pretty damn good at spamming search engines, so searches related to online gambling will make 888 stand out. 888 also has an annoying little sister, Grief Club, well known for jerking players around while big brother 888 says, "she ain't my sister, what can I do about it".
Just as useful for a beginner is to know where NOT to play, many rogue operators do their best to look famous and reputable. It is no good reading the casinos own site to get the truth, every single online casino is either the "biggest", "oldest", "most reputable" available, but much of this varies between exaggeration and outright lies.
For a beginner, decide what software you like, possibly by joining one casino from each provider in the accredited section. CAREFULLY read the terms and conditions, especially for the new player bonuses on offer, and remember that many will ask for photo ID before making the first withdrawal if it is of any size. Some European contries are taking the same view as the US, wanting to make online gambling illegal, so best check first, although it is not currently a problem. If over 18 but under 21, be especially careful with the term "of legal age", some casinos have shafted under 21's with this, even where 18 is the legal age in their country, and it has been a fight to get redress. Check also currency rules. Casinos now expect players to use their own currency, and believe the standard currency of Europe is the "Euro", and players whose countries have not adopted the Euro may fall foul of this by using the US$, where the casino believes it should have been Euros. This used to be a problem only with non-UK players using our Pound to screw bonuses, but casinos are using the rules more widely now - and you only find out when you win.
Naturally, a shill will know this already
New members need to be careful how they word their first post so as not to be assumed to be a shill for a particular casino. Using "online-casino" as a nickname was not the best move either
...only if you shake it for too long...! 
