(1)you often won't collect the 250 D because they don't have it,
No, 250 is quite rare from smaller countries, especially in the beginning.
But somewhere in the range 100-200 is VERY common and since you don't have any allies you must share the money with it does give a LOT of extra money, which you desperatly need in the beginning.
Remember that this money goes directly to treasury without adding any inflation and 150 D is 3 new Tax collectors for those 3 new provinces ...
(2)you can't attack for 5 years after the peace
*hint* It's very rare to only border one single foreign country ... =)
(3) you leave an enemy at your rear as you advance. Of course, you're probably safe for 5 years since they would also take a huge hit to stability if they broke the peace and since they've been pretty well decimated by you already they won't be able to build much of an army.
Add to this that you have just cleaned out their bankaccount so they have 0 money in treasury ...
This usually breakes their back (they fall behind in tech etc too vs you) so they don't hassle you for hundreds of years unless you deliberatly provoke them.
BTW, you do go back and finish them off after 5 years don't you???
Depends, sometimes yes sometimes no.
As I already said, usually they will not really bother you at all for the rest of the game anyway, since they are usually much weaker then you. If they do, you even get "FREE" provinces BB vise (0 BB for taking provinces in defensive wars, unless you do a full annexation).
As an example, playing Russia.
I usually take 3 provinces from Kazan, taking the 3 ritch center provinces from it and leaving the country split in 2.
This gives a lot of VP and also minimizes the border towards Poland-Lithuania, which you sooner or later will be fighting (thus you won't have PL armies sneaking past you and wrecking havoc in you "backyard" provinces). The split country of Kazan will also have 0 chance to defend itself if it would try to DOW you later on.
Attacking again to get only vorones or a full annexation is IMO not worth it, economically or BB vise.
GH however, taking 3 provinces in a first war and then returning 5 years later (you can attack Astr meanwhile and then even Sibir if you got time) is good policy, since the GH capital has a goldmine ...
I had always annexed when I took all provinces, wanting to expand rapidly not considering the negatives (worse BB and general relations)or the money.
If your playing for VP, also don't forget the severe reduction in VP a full annexation yields.
A 7 star peace gives 14VP (2 per star). If you do a full annex that is all you get. If you take 3 provinces you get VP for each province too, equal to the income visable when you click on an enemy province. This can yield 30+ extra VP if you get rich provinces.
Ie you loose a LOT of peace agreement VP by full annexation.