Danby is excellent (three models), Haier reportedly had troubles but seems to be improving, and some of the folks here can advise on US brands.
A combined washer/dryer in one unit, in a compact size with sink hook-ups, is a difficult item to find.
The closest you're going to get to a compact combined washer/dryer might be the Danby Twin Tub, DTT-420, which is an excellent machine but is not fully automatic. You have to transfer the load manually from the wash tub to the highspeed spin-dryer and back again (once after wash, once after rinse). I have one, it does an excellent job and it's fast, and clothes come out almost completly dry (get a drying rack, they'll hang dry quickly, overnight in winter or in hours during summer). The mechanicals are quite simple so it should be reliable. Viable load capacity is about 7 lbs., not 10 (all compact washers seem to over-estimate capacity, I don't think it's a conspiracy

. Cost ranges from $250 to $350 depending on where you get it.
Another option is the Danby front loader, DWM-5500, stacked with the matching dryer. This is a fully automatic front loader of the type that has started to become conventional in the US now. I have the manual around here somewhere but you can find it on
www.danby.com if you want to check about whether it can be used with a sink connection. It gets rave reviews, everyone who has this machine loves it, and it has a 200-degree wash option (useful in cold & flu season). If you mount the dryer on top of the washer, chances are you'll want to install it permanently near the sink so you don't have to move it around. Also note that front loaders cause a bit more vibration than top loaders (the other two models here), so if you need to worry about the neighbors hearing it, this might be an issue.
Last but not least, Danby DWM-99-W, is a compact top loader with normal automatic cycles. Does not have a separate spin-dryer or other built in drying funciton aside from the normal spin function at the end of the cycle, which is not a highspeed spin like the twin tub has. (Again, get a drying rack, and assume it'll take a bit longer for clothes to dry compared to the twin tub above). Price range is similar to the twin tub. Size is a little smaller, load capacity a little smaller also. The few reviews I've seen on this are very positive also.
All of these generally have to be ordered via internet unless you're lucky enough to have a dealer nearby (see also Absolute Appliances in Southern CA, which is where I got mine from, and had it shipped up north to me).
Note, all the Danby units have a conventional pump to discharge used water into the sink. Some other brands offer less expensive machines that use "gravity drain," which means there's no pump and you place the hose on the floor next to a floor-drain. This is fine in basement laundry rooms with floor drains, but in an apartment, you'd have to discharge the water into a bucket and empty it into the sink, which is a lot of effort. So if you're buying something other than Danby, check to be sure it has a drain pump and can drain into a sink.
If you need more info on any of these, feel free to ask.