1.Tony Kart
2.Intrepid
3.Arrow
4.Maranello
5.Birel
6.Sodikart
7.CRG Road Rebel
I would gladly race any one of those karts. Performance-wise you won't be able to find much between them, particularly as a beginner. Any one of them can win.
An important part of your consideration should be spare parts availability. I think from your list at least Intrepid, CRG(+Maranello), and Birel should have good parts availability in the region.
Inspecting a kart yourself there are some things you should look for that are easy enough. Look carefully at all the weld points, particularly at the back of the chassis, which is where cracks most often occur. Also look out for different color paint which would indicate a crack and a repair.
Look under the frame to see how much the frame has worn out. If the tubes are more square than round you've got a kart that's seen a lot of use. Serves as a good bragaining chip if you feel the kart is still good.
Another thing to look for are brake pads, and if the brakes work properly. If the brake pads are almost worn out that's another hundred or two you can bargain off the price. The brake pedal travel shouldn't be very long - ask when the brake system was last bled. You don't want to have to start doing a brake system overhaul after you buy the kart.
If the kart is filthy when you have a look at it that's an indication that it probably hasn't been looked after very well.
Put the kart on the ground with tyres on it. Grab the back of the kart and wiggle it sideways - you're looking for movement in the rear bearings. If the axle stays in place and the chassis moves side-to-side the rear bearings are gone.
That's just a few tips. Those in Singapore will know better about the parts availability over there. To find out yourself you can ask the local dealers "can i buy a set of rear brake pads for XXXX brand XXXX model kart right now, or do you have to order them for me?"
For the engine there is no real way to know until you open it up, or if you trust the seller 100%. But again as with the chassis if it looks filthy it probably hasn't been looked after very well.