All round newbie to DnD
Tying your character into the story would depend on the specific story - different GMs will use different settings and there's also the other PCs to take into consideration, how well your character might get on with them and stuff like that :). Whether or not the stats etc are "good" will also probably depend on the nature of the specific game, like whether a certain ability will be useful in combat - lots of Cleric abilities tend to be good against undead but if you find yourself in a campaign with no undead at all, such abilities will probably never get used.
Unfortunately I can't really offer any guidance on the mechanics since as I mentioned, I've not got round to trying 5th Edition yet - most of my experience has been with its immediate predecessor (which lots of people hate, though I'm not really sure why - personally I find the first two editions horrendously complicated and don't like them very much ;)). I've heard 5th is generally pretty good, though, not too complicated or anything.