Ships & Modules

L2 > Arbitrator
L3 > Prophecy

Unless you know exactly what you want to do with the character, not focusing in the beginning is not necessarily a bad thing. The main thing I think you'll run into though, flying Amarr, is that you won't have a lot of options for damage unless you train up your drone and missile skills as well.

Drones are kind of a given, every faction uses them to some degree, and in the right ships they're hands-down the way to go.

Lasers are a little more iffy in my book. I started out Minmatar and loved having access to all damage types in my racial starting weapon. Like others have mentioned, you'll find yourself slightly annoyed or taking a little longer against enemies who are tanked against EM/Thermal damage.

Something you might want to consider is cross-training in a limited way* which gives you options and access to some better faction hulls, but still capitalizes on skills you're already training. Given that you're going Amarr to start, Gallente is what I would cross train into if I were you - both races have some nice drone boats, use primarily armor, and this will give you access to the Sister's of EVE faction ships (which also use drones, lasers, and armor - plus exploration bonuses as a role bonus to make some more isk without having to dump a bunch of skill points).

*when I say cross train in a limited way, I mean that training something like Gallente frigates/cruiser each to level 4 gets you 80% of the bonuses, but only takes a couple days (level 4 of a skill is only 17-18% of the sp required to get level 5). Same goes for some T2 stuff - you won't even be able to fit it until you get the support skills up, so you'll be using Meta's until then, so why bother training to use T2 stuff you can't fit yet?

Personally, when I made my last character, I also made an Amarr guy. SoE ships weren't out at the time so I went Sansha ships. I would do level 1's and 2's in a succubus, then swapped up to a Phantasm for level 3's and 4's, all using passive shield tanking. Never bothered with anything bigger than cruisers on him, but a Nightmare might not be too far off now that faction hulls are so much cheaper than they used to be.