Hi, and welcome to Pathfinder, the game I know way better than I really should!
First, let's have a
guide to the Paladin. Also, lets' have a
guide to all the guides! Those are really good resources for seeing all the things you can do with your class.
Second, you called the Aasimar a "template" which was a bit confusing - because template is an actual rules term, and refers to things such as having the Half-Dragon template. Templates aren't usually allowed for player characters, in case you were wondering. Likewise, Angelkin Aasimar etc. aren't "templates" but in common parlance just called "variants".
No worries though.
Third, do note that all the Aasimar variants
only replace the ability score modifier, skill modifier and the spell-like abilitiy - you keep everything else from Aasimar, so you very much keep resistances and darkvision. You can even take alternate racial traits that don't swap out skilled or the SLA, so you could be a Scion of Humanity Angelkin Aasimar.
You're right that Daylight can be a good spell - but not because it produces light, that can be done by the 0th-level "light" spell which your party can have if they have any spellcasters whatsoever. It's not even that good against undead, since it doesn't count as daylight for the purpose of, say, destroying a vampire. And Alter Self is a really good spell, it can be good in combat but also help you with disguises and such.
As for weapons - the Greatsword does 2D6 damage, which averages out to 7. The Bastard Sword does 1D10 damage - which averages out to 5.5 damage, and is actually as much as a small greatsword (for a halfling or such) does.
Nobody really compares the bastard sword to the greatsword - if you want to wield it in two hands, the greatsword is clearly the superior option. Some people do occasionally want to take the bastard sword instead of a longsword to wield in one hand - and then people point out that 1D10 is only 1 more average damage as 1D8 (which a longsword does), and that +1 damage is
really not worth spending a feat on (heck, weapon specialization gives +2 and is still considered a pretty bad feat).
The Bastard Sword may be Ragathiels favored weapon, but that does not by default have any gameplay effects - it does for Clerics (who get to be proficient with it, and free proficiency actually makes the bastard sword okay) and in some other rare cases, but none should apply to you and a greatsword is basically the same thing flavor-wise.
So bottom line, you're fine with a greatsword. It's a good weapon, doing the highest average damage of all non-exotic two-handed weapons while having a decent chance to land a critical hit.
For more general build advice, take a look at the guide I linked, or some of the other Paladin-guides.
Oh, and a last piece of advice: Make sure the other players have fun with your playing a hard-ass Vengeance-style Paladin - don't always give them a hard time for what their character does, or take over every scene with your own characters morals. Focus your vengeance more on cases where it's really deserved, and don't forget that Ragathiel also stands for chivalry which does include letting others have a first go at things. Mostly, just remember to let other players have fun too - and I' mostly saying this because there's some negative stigma on that kind of paladin, not because they're inherently unfun to play with.
) Not sure if your stats were rolled or point-buy, but if the latter, if it were me I would bring that INT 16 down a notch or two to bring the WIS up to at least average.