For someone who was in the car business for a long time, I don't see a lot of sense in the above post, certainly not for a consumer. I'm sure when BMW's lowest model became "prestige", either. It's still a shopping hatchback, for the most part.
There's margin in everything, but less in used vehicles than new.
In terms of asking for a discount, be as cheeky as you like. There is a school of thought that if you don't offend the salesperson with your first offer, you started too high
For one thing, the dealer is chancing it a bit when they set the advertised price in the first place.
It is best if you have some leverage on your side - does it look like there is going to be a significant bill in the near future, e.g. how long until the next service? Are the tyres worn? (Another thing to look for is uneven tyre wear across the width of the tyres, if so it might need wheel alignment sorting out.)
If not a discount, what can you get thrown in? As above, what about next service included (good for the dealer if they know you're going to be a recurring customer)?
Research (which you've already started doing) - what other models are about for similar prices? You may not want an Audi A3 but the BMW dealer doesn't need to know that.
Is there another dealership close by? After chatting at the first dealer, thank them and tell them you're looking about. If they're eager to sell they would rather cut a deal before you leave the showroom.
Ultimately, have a figure in mind that is the best for you, the figure that is acceptable to you, and the figure that would make you walk away. Aim to get your best, settle if you can get the acceptable, but be prepared to walk away if the deal doesn't get past your absolute limit. There are plenty of 1ers to choose from, they're not a rare car.