Is it a good idea to pursue a PhD in Singapore as a European student?
About point 1, it probably depends on one's field but Singapore is a nice place to graduate from. I really enjoyed the department there and working there in general.
About point 2, it should not be the only reason to do a PhD there but Singapore has a unique feel and is a very enjoyable experience in itself. As anecdotal as it may sound, the food is cheap, eclectic and very good.
A few caveats :

While life itself is kind of cheap in Singapore (eating in food courts is cheap, making your own food slightly more expensive), housing is expensive. You may need to share a flat with flatmates (that can be a very nice experience by the way, especially in a new place).
Having an immigration pass to do a PhD is, of course, not a problem, however your spouse may not get a pass (it depends on your income and I have been told that a typical post-doc salary is below the limit). You might want to check that if applicable.
From what I have seen both in Europe and Singapore, I would say that there may be slightly more pressure on PhDs and  post-docs there than there is in Europe (of course Europe is a big place and it mainly depends on your supervisor).

Obtaining a post-doc in Europe/USA with a PhD in Singapore is not a problem in itself as long as you make sure you meet some professors working in Europe/USA and get yourself invited to some seminars when you're in Europe/USA. That is where the 'large budget for this kind of things' you talk about in the comments will come in handy.