$1k for most of the above kits is the price without cymbals. For example, the Gretsch Blackhawk goes for around $950 for the set, hardware and two cymbal stands. If you want decent cymbals, you're looking at an additional $700 minimum. As a general rule, avoid brass cymbals; cymbals made from B8 alloy are cheaper but may not sound as good as B20 cymbals. Most pro-quality cymbals are made from B20 alloy.
For the set, I wouldn't worry too much about tone. A fresh set of drumheads and some good tuning will make your drums sound more than decent. For cymbals you do have to take into account the fact that you can't really alter the sound of your cymbals so if you're looking for tone, you have to take that into account, and there's a strong case for buying good quality cymbals from the start. At the same time it's almost a given that your taste in drum sounds hasn't completely settled yet and there's little point in splashing out a large sum on cymbals you may not stick with.
In guitar terms, you can see this as: an electric guitar's tone will be affected by the wood and the build, but much more heavily affected by the pickups, the effects, the amp, and the quality of the signal. This is like an acoustic drumset, where the build needs to be of good quality but the heads and tuning make or break the sound. An acoustic guitar's tone, on the other hand, really is primarily dictated by the tonal qualities of the top and body. This is like cymbals, and it's difficult to alter the tone if you don't like it. If you're in the habit of listening to the drums and know what tones you like, that will be very good because it's less likely you'll end up with quality gear you don't like. Otherwise, it's like buying a $4000 acoustic guitar with a cedar top and deciding you like spruce top guitars better. The upside, of course, is that a well-made guitar will always have resale value. Similarly, you will easily find buyers for good quality cymbals.
Anyway, having said so much, the whole point of my post is, you still need cymbals, and if the cymbals are coming out of your $1k, you won't get either durability or tone. Even then it may not be wise to dive in the deep end.
My personal recommendation - for your budget, assuming you want both drumset and cymbals within $1k, I'll put in a vote for my own drumset, the Ludwig Accent CS Combo, around $650 (not sure if Swee Lee still brings them in, though). You might also look at the Mapex Q or QR series, though I'm not sure how much they are (Drums Resources Music Place, at Excelsior). I personally have Sabian XS20s, which are good value B20 cymbals, but B8 cymbals will generally do the job. Other very low end kits such as the Pearl Forum may come with brass cymbals - depending on your needs, these may be better options. For practice only, especially in Singapore, consider the Pearl Rhythm Traveller: small, compact and you have the option of using mesh heads so you don't disturb your neighbours.