You could use any standard utility pump or even a pool cover pump. Both would bring the water down to at least one inch and save you the trouble of bailing. A garden hose could be used on either model and run to the sink or outside. What water is left over could then be sucked up using a good sized wet vac..say a 12 or 16 gallon. Trouble with this sized wet vac is that it gets very heavy when full of water.

Trust me I know...I spent several hours helping an elderly neighbor who was getting water in his house...we had two 16 gallon shop vacs going to suck up water coming into his family room. I bet we emptied both of them over 20 times...he did not have a floor drain so they had to be lifted to his utility sink.

Does your laundry sink drain go into the floor?
If yes, then you could install a floor drain nearby and connect to the drain line. If ever you get water, a push broom or floor squeege would help get water toward the drain. Never a fun situation but you need some way to get that last 1" out.

A utility pump would work pretty good.

I have a shop vac that can also pump water, which came in VERY handy when I had to install a new sump pump in a pit that quickly filled with water after I pumped it empty.

Any submersible utility pump will work, doesn't have to be a high flow rate really although of course it will take longer to discharge. I pumped out my flooded basement on monday with a small Little Giant AC pump for 12+ hours straight. It's a small pump with a standard garden hose output made for draining pools. This would work well, can be anywhere from $40-$80+ for a decent one. If your basement is unfinished and you have a good backup drainage system so the water doesn't get TOO high, you can go the AC route. Otherwise, you might want to consider a 12v DC motor utility pump or perhaps better a battery backup Sump Pump or a municipal water backup pump (if you're not on a well).

You might even consider as a backup looking at a marine bilge pump for boats. Uses a 12v DC source (aka car battery) and most can be run via a manual switch or a automatic float valve. Check any marine or boating store...

Jay

thanks for the advice, folks. A pump it is.