How much can I expect to pay for a small engine rebuild?

The fluid coming from the spark plug hole when removed could be fuel. Cost to rebuild small engine would be minimum $1000, get somebody to check it over and quote before they repair then you will be able to figure out if it’s worth repairing or replacing.
No fuel coming out of the spark plug hole is not a bad thing,if no fuel was coming out, then the spark plug would have nothing to ignite. Just take it to a mower shop and get them to quote you for repair, you should not try this repair or diagnosis yourself.

just take it to a lawn mower shop and see what they think.
they know those engines.
you didn`t say what the fluid was.
oil, gas ?
if its gas then you have a carburetor problem.
does it run ?

edit:
if it is just fuel coming out then that is good.( best scenario)
you just have a carburetor problem
letting fuel run free into the cylinder.
If it turns out to be just that .no big deal.
once you fix that ,check your oil to see if it has gas in it.
the fuel can leak past the rings and into the crank case and into the oil. If so be sure to change the oil.

if this happened after the mower sat unused over the winter the valve in the carb could be stuck open letting fuel run into the engine.

Dollar wise your best bet could be, purchase a new mower, There are some good bargins on new ones right now. They will deliver too. To get your old one to a repair shop, the first expense would be them coming after it. Put a for sale sign on your old one, some shade tree mechanic will come by and relieve you of it.

I f you can do the work your self. There are outlet stores that will sell you a new engine that will fit any mower, for less than you can get one overhauled.

a replacement engine is about $500 and $100 to install.sounds to me like the carb is gummed up and flooding. if you check the oil it is probably over full..the fuel has leaked into the crankcase and thinned the oil its slipping past the rings. that’s the white smoke..$200 fix at a lawnmower shop.if your going to do it yourself. take off the carb. clean it with carb cleaner. get the engine #’s and get a carb kit. you need a new float needle..change the oil and filter. put in a new plug as that one will foul soon from burning oil. also check the air filter to make sure its not oil soaked. this is very comon in the spring after the mower has been sitting up.next year run all the gas out of the engine before putting it up.

Before you do anything expensive check the oil level and make sure the engine is not over filled. The oil level needs to be exactly at the line on the dip stick not above or below. If the oil level is above the line the engine will burn oil just because its overfilled. You haven’t given enough information to get an estimate on a rebuild. http://www.stevesequipmentrepair.net