I know that each time we level up we get more stats in health, magicka and stamina, and that we get an attribribute point to level one of those up further, but I am wondering if these attributes are also affected by our choice of class? Or race? I haven't seen mention of it anywhere.

If not, then you could create a dragonknight or a sorceror, dump all points into health and they'd have the same stats (exclusing gear of course) at level 50?

I think so, but maybe someone else knows for sure.

Class and race choice does not impact the attribute points you receive either at creation or per level.

All characters and classes start with 100M/100S/150H. A DK with all his points in health will have the same HP as a Sorc who did the same.

Yes, everyone start with the same stats. I am not sure about the game mechanics around soft cap if that is same for everyone, but should be so.

Soft cap is when your 1 stat point start to generate less mana(example) for each point you put in magicka.

Here's some good info on the attribute points and scaling:

http://www.reddit.com/r/elderscrollsonline/comments/1y8f09/concerning_magicka_and_stamina_damage_scaling/

Racials are passives you can spend skill points in. So for example if you pick a race that has as one of its racials an increase to health, by spending skill points on that racial you will increase your health.

Their stats might also vary based on the skill points you put into various skills (including racial passives), but assuming that those are the same, the final total would also be the same.

Ok cool that's good to know. Very different to other MMO's but in line with the other TES games.