The Submariner is an excellent first choice as a first "good" watch.
The date version was first produced as reference 1680 in the mid-sixties so it's hard to say if it’s more "classic" or not. Certainly Sean Connery in the Bond movies was wearing without date, but then again the first movie with a Rolex was Dr.No that came out in 1962.
I personally would prefer a new Rolex (or any watch) with a date function and especially with Rolex, the "Cyclops" date magnification is a unique look. Having said that, in my experience they scratch more easily because of course the glass sticks out (although today sapphire crystals are so hard that it's almost impossible to do).
The Sub Reference 14060M "No Date" was almost discontinued this year but Rolex decided to keep it alive. You won't find it on their official website though..It also doesn't have the Ceramic bezel which the new Rolex Submariner 116610LN with date has.
Whatever you choose, make sure you get the last reference numbers and not some older models..
In terms of "sensible price" - I'd say grab one quick, as the Swiss Frank is very strong... I haven't bought a Rolex for a while, but I would say that you should be able to get up to 10% if the dealer is keen and you can pay cash, there won't be much more "room" and in fact Rolex won't actually officially let them give any discounts or they'll lose the right to represent them.
Rolex is more available at various shops so there will be a lot of possible sources..I personally like Wempe on Bond Street. By the way, Rolex has opened their own Flagship store at One Hyde Park, might be worth a try as they may be more flexible on the price. Online you could try http://www.bankslyon.co.uk.