For $3000 , you can get a lots of foldies with better conponents for better shifting of gears. You may want to check out MYBIKESHOP for both TERN and DAHON Bikes and MightVelo for BIRDY. For TERN look at the P and X series.
I have a friend who bought a Giant Road bike when he was in Taiwan, He told me it is cheaper to buy from there.
Do noted that if you buy from overseas, you will not have any after sales support or wannanty.
3k is quite sufficient generally, but it will depend on several factors. I bought wifey a Travelo (can't remember whether it's FS-S or FS-V - key specs : 20" wheel, 1x10 Deore, <10kg weight) for less than SGD$1k. I also see assemblers selling Crius-branded bikes for less than SGD$1k (I ride Crius Velocity 451 wheel, 2x10 Tiagra). Before getting those, I went to check out Dahon, Tern, Brompton (and some of the -inspired versions too).
Cost factors : 1) Brands and model - no need to elaborate 2) Wheel size - generally it will be compactness vs riding comfort, bigger generally more comfortable (but also influenced by tyre width and air pressure). GENERALLY 3) Specifications - choice of tyres / wheels (general purpose / stock vs racing), gear system etc. My wife is pretty happy with 1x10 (only rear gear change); I need 2x10 for personal preference as I like to keep my cadence constant and I ride more varied environment
As for overseas imports, I was exploring getting from Taiwan some time ago as I was visiting. The main reason which dissuaded me was the transport cost (it will not be a simple 'check-in luggage' and you do not know how the bike will be handled). Also at that time, I did not know enough about bike assembly. Even now, I would think that the savings will probably be insufficient to entice. But then, I have been buying second hand bikes.
You can chat with me if you need a bit more details. Safe riding.