At their core, Paladins are holy warriors. They are a chosen god or goddess's enforcer; embued with divine powers and abilities in order to serve their deity and deliver the deity's wishes to the furthest reaches of the realm. This is also where you start seeing a lot of the restrictions that come onto Paladins on the role play side. Paladins, by definition, are devout. They follow their god(dess)'s teachings, and often to the letter. If their god is all about killing every opponent that he/she faces, then guess what his/her paladin is going to do?
Because of this, you want to be very careful when choosing the deity for your paladin PC. Talk about it with your GM, go over the gods that are available - and whether or not you're allowed to make up your own. Go over the codes that each god teaches, what they expect, and where the boundaries on actions are. Someone who worships a god that teaches to accept fate is likely going to be more against resurrection and raising the dead than someone who worships Gelida the Resurrected.
The choice of deity can, and should, inform all other decisions you make on your character. So don't be afraid to start here. After all, the beliefs and views of the god will affect you in more ways than just actions taken. A god of guile and cunning will likely favor stats that increase your Wits and Agility over your Strength and Endurance, while one who is all about brawn and might making right will probably want the exact opposite.
This is one of the common complaints people have about Paladins. I'm not sure where it started, but it seems to stem from the way some people play Lawful Good and view just what exactly Lawful Good means. Now, by definition - though the new books may have strayed from this, so I'll be quick here - Lawful means that the law, or some form of order like a code of honor, is important to your character, and Good means that you try to do the right thing and what is Good and Proper. This doesn't mean you have to be a moron. It also doesn't mean that you have to be a nice person. It simply means that you server Order over Chaos, and Good over Evil. Within that purview, you can be a huge dick or tool. In fact, you may end up being one just due to the self-righteousness that can come about from this view point. At the same time, this doesn't mean you have to be a dick, you can still be the idealistic nice guy.
This is one of those things where an example may be in order. So, let's go with two. Both Optimus Prime and Superman are Lawful Good characters. They both believe in, and fight to uphold, the law and their own personal codes of justice and morality. They both fight for the greater good, for personal freedom, for truth, and for justice. However, while sticking within those boundaries, both have a lot of leeway in how they approach things. Superman is often called the boyscout because of how friendly and polite he can be, and his always trying to do the right thing. However, in his actions, he has also acted as a world class dick to some people. Optimus Prime on the other hand, acts downright villainous at times in the Transformers movies, but never does anything that would break a Lawful Good alignment either.
So, just remember. Lawful Good does not mean you have to be dumb. It also does not mean you have to be nice. It just means Law and Good are where you have sworn your allegiances.
A Code of Honor
This is mostly covered in the above bit, but I just wanted to point it out. Being Lawful means that you have some code. Now, this could be the law of the land, but more often it involves the views of your god. A Lawful Good god that is ok with slaves, is unlikely to have a Paladin that is against slavery. This is also something you want to talk to your GM about. Discuss your character's code when you discuss the god. Make sure that it meshes with the GM's expectations, and that you aren't going to be blindsided by a conflict in viewpoints.
Mechanical Power / Role Played Restrictions
Paladins, no matter what they're called in your system of choice, tend to be very powerful mechanically. Just looking at the classical D&D paladin, you have something close to a fighter's progression for combat and the ability to use heavy armor, the ability to heal with laying hands, immunity to toxins and poisons, and at higher levels the ability to turn undead and cast divine spells. All of this power comes at the interesting cost of role play restrictions. That code of honor, and the beliefs of the deity, that we discussed above are going to chafe you. You, rather simply, do not have the full range of options available to you that say the Rogue character does. Some of the things that those people would do, are quite simply things that your paladin would never contemplate or allow themselves to do. However, this isn't necessarily a bad thing, and in fact can be where the fun comes in.
Crisis of Faith
This is as much for the GMs as it is the Players, but some of the most fun you can have with a Paladin character, or any character that has a stringent code of honor, comes when that code is challenged. Put the character into situations where they have to choose between following their code and getting what they want. Between their code, and doing what may be viewed as the "right thing" by today's standards. Have opponents ask for mercy, or otherwise come for help (should they survive an encounter). These moments of choice are the moments when the paladin gets to shine. Especially when, due to their code, they take the hard path. That ability, the resolve to take that hard path is also what serves to make these characters so inspiring to others, and potentially some of the most memorable characters you'll ever play. After all, how many people would actually go out to single handedly face an army just because it was the right thing to do?