The critical measurements are that you have to match the rim diameter to your brakes, and the width of your hub to whatever your frame needs.
A 27" wheel may be several different sizes. Its best to use the ETRTO number which is 622-xx for a 700c wheel and 630-xx or 635-xx are nominal 27 inch.
So your existing tyre/tube will fit because the new wheel's rim has to be the same size as the old one. Nothing else will do unless you want to risk needing a brake replacement. If you have disk brakes then its a little more forgiving, but still not a good idea.
Also the new rim's internal width should be pretty similar to the width of the old rim.
If your existing rim's okay then you might choose to replace the hub and rebuild the wheel. Its possible you need shorter/longer spokes at this point, and there's certainly no cost saving over a complete wheel if you can find one.