I do not recommend cleaning your gun while it is assembled. Field-stripping the gun can be a little intimidating to a new 1911 owner but after a little practice it will become old hat. I distinctly remember 9 years ago making a HELP call to a friend for advice and instructions.
When I disassemble mine, I remove the slide with the recoil spring assembly intact. Put the beavertail in the joint between your thumb and index finger. Wrap your fingers over the rear sight and ejection port and squeeze the slide back out of battery. You may have to use your off hand to cheat the slide back a little. This position/technique will give you decent leverage to hold the slide back while you push out the slide stop. Then just ease the slide forward using your off hand to wrap completely under the slide as it comes off. This will help trap the recoil assembly from flying across the room.
When reassembling the gun leave the plug out and the bushing installed 90 degrees to the ejection-port side of the gun. Install the recoil rod and spring as normal, with the spring poking out from the muzzle end of the slide, past the muzzle. Now install the slide assembly onto the frame.
Next, install the slide lock through the frame, barrel link, and slide notch. Be careful. Until you get the hang of it it is easy to slip and "idiot-scratch" the frame and slide. Until I got the hang of it, I put a business card on the frame to act as a scratch-guard. The recoil plug is out so there should be no tension on the recoil spring at all.
Take the little orange plastic safety-plug do-hickey (which seems to come with every gun) and put it in the chamber. This keeps the pistol out-of-battery and I'll explain why to do this later.
Now place the recoil plug onto the recoil spring. With the gun on end, with muzzle pointing up, install the plug and turn the bushing to trap the plug. Some people find the easy to do with bare hands and some people prefer to press it in using the flat of a (plastic) bushing wrench. Be careful that the spring and plug don't slip and spring up into your face. It happens.
The reason I use the safety-plug is that with a match barrel and bushing the fit between the bushing and muzzle is pretty snug. If you take the gun out-of-battery the barrel moves forward slightly to a looser-fit area. Turning the bushing is easier. If you do not have a snug fit between your bushing and muzzle, this isn't really a concern. This may be an unnecessary step/hint, but I figured I'd throw it out there.