Ships & Modules

i did that.
dont do that
cross train.

It really really depends on your playstyle and what you want to do w/ your toon.

I fly w/ plenty of guys that are one-race. They fly the same ship(s) in every engagement and do either really well or really poorly.

The plus side of purity: you get to know your ship really well and are forced to figure out how to maximize it. You'll understand the fights you can/can't win and you'll be able to plan accordingly

The minus side of purity: you are forced into certain roles in a fleet/gang because of your limited ship choice and you'll know before hand that you'll go down in a blaze of glory in your completely inappropriate ship/fit

Plus side of diversity: you get to fly whatever the flavor of the month is, you are (almost) always able to get a ship that meets the fleet doctrine and your hangar looks very pretty

Minus side of diversity: time consuming, time consuming and time consuming. My toon is 10 years old and I've just a couple years back gotten myself into EVERY sub-cap ship. Its also semi-expensive, as you'll have to buy skillbooks for every skill in the game. Sometime choice can be overwhelming and you'll stay up til 2 in the morning on EFT nit-picking 3 ships with 3 different fits each trying to nickel and dime the most DPS while also considering the aesthetics of gallente vs. caldari.... true story

Your notion no cross-training is misconceived. In order to train for "pure Amarr" you need to train:

Fitting/Navigation/Capacitor/Gunnery support skills*
Amarr ships
Lasers
Drones*
Short range missile systems (Rockets, HAMs, Torps)*
Energy Neuts*
Tracking Disruptors

All of the skillsets marked with a * are used by other races as well.

Cross-training Amarr/Gallente is borderline trivial as you'll already have good support, drone, and armor tanking skills.

Cross-training Amarr/Caldari or Amarr/Minmatar is a bit tougher, but you'll still already have good support and missile skills.

Overall, Amarr are in a good place in terms of flexibility. Their T1 lineup has laser and drone ships, and their T2 lineup adds missiles. They're not the ZOMGWTFBBQ solopwnmobiles of yore, but barring any radical changes they'll be useful for the foreseeable future.

Legion
Guardian
Zealot
Vengeance and retribution
Slicer
Harby
Abandon
Are some of the best amarr ships

Amarr is about damage application and tank
Also lasers are the most flexible weapon system in the game both pulse and beam are good
You will whant a few sheald tanked ships for thows fleets

I see myself as a pure amarr character. Although i now have ship skills for all the 4 races because the changes with the destroyer/battlecruiser skill to racial destroyer/battlecruiser

When I started playing this game I picked Amarr 'cause in my opinion they had the nicest looking ships. So I started training Amarr ships, armor and lasers.
After something like 10 months I joined my first null sec corp and back then nano fleets where the hype. that was very convenient 'cause at that point my lazer and armor skills where already pretty high. I could fly all T1 subcap and up to T2 cruisers decent.

So shield skills was the new things to train, i really wanted to fly that wonderfull nano zealot. After maxing out shield skills. I went for drones and after that missiles for those few amarr missile boats. Somewhere in between I did some ewar for the neuting and TD ships.
And now my main is amost 3,5 years old and i already started training cap ships the last 2 months.
I just wanna point out with this that if you wanna go that way. Amarr is more than just lasers and amarr like people say. If you wanna go for the whole amarr line than this.

And about your question if it's gonna hurt later for pvp. i never had a fleet that i couldn't join because i was amarr. they have some of the nicest ships in the game and a lot of alliance use them in doctrines. But there really shine in group. For solo pvp the're better races.
Also like somebody already stated: the lesser ships you fly the more you fly with them. The better you start to know them and the better you get with them.

Edit: I really need to learn to first read the comments before I post the same stuff that somebody already said before :p

No and a little is your short answer.

Now the long(er) answer.

No - Why?

The Amarr have a mix of everything you or almost everything you might need later in your progression, so stick with it and squeeze out everything that the Amarr ships offer to you.

Amarr ships have laserboats which require you to train the turret and the support skills, they have missile boat which require you to train missile skills and the support skills and they also have drone ships, which require you to train for drones.

So even if you stick to Amarr for a long time, it won't hurt you at all and if you decide later that you want to try out different ships, that's fine since you have your basics covered and the only things lacking are some different turret skills.

A little - Why?

You miss out on some really cool pirate faction ships but there is usually no reason to skip them for the time being and get to them later.

If you like what you are doing and you decide to stay you will figure out very early that you invest a ton of time here. So to keep you here you can restrict yourself to not crosstrain until later so everytime you train some ships later there is a new world opening for you even after a long time.
Well, that's what I did.

A corpmate of mine a very long time ago told me that the best thing to do was to stick with your first race or pick a new one right off the bat and train exclusively that race and your general support skills until you can fly command ships. By that stage you will have a lot of SP and will have pretty much mastered your chosen race.

Now you can cross train ships and weapons and it will be super quick, since your support skills will be used for pretty much everything you do going forward tons of those SP will transfer over when you do cross train. At this stage I'm just finishing up my 4th race and all I need to train are the spaceship command and the actual guns for each race. Was a very long haul at the outset and after finishing my second race I did move into training an Archon (to level 5) before going back to cross training.

I probably wouldn't say that you need to go as far as command ships, especially considering the leadership skills you need to train to get in one now if you didn't get into one before but the underlying advice was good. Focus on being good at only a few things early on and branch out later when you can't go any farther in what you've started with. If you are unfocused you will be less effective than you SP count would indicate as you are half decent with a ton of things rather than super proficient with what you are using. Any race can work but I feel Amarr can be a pretty bumpy road if you intend to solo. The tragically small number of mids on a lot of Amarr ships make them less useful for solo than a ship with an extra mid for the loss of a low. A 2/3/5 or 3/3/4 slicer would be a true god machine and the two mids on a Punisher are what holds it back even though the slicer can make two mids work. Amarr work fabulously well in packs though.