Nice looking mower. Appears to be in good shape, particularly the reel. Appears to have been sharpened with a relief grind in the past. Only the leading edge of the blade is bright, rather than the entire edge. Looks like it could use a back-lapping, however. That being said, let me focus on the engine. First, the Honda GX is a great engine. Your mower is 24 years old, and a new Honda GX would last at least as long. However, the Honda is a serious piece of change. The Briggs 9 CID "Classic" is also a competent engine, and unless abused should have plenty of life left. Here's what I would do: 1) Remove the carburetor, and then separate the tank and carburetor. The long plastic tube is the main pickup, which lifts gasoline from the tank via diaphragm pump and spills it into a small well directly underneath the carb, The second pickup is a casting projecting into the small well in the tank. The long tube has a screen on the bottom, and it must be free and clear. You should be able to blow gently on the tube, On the other hand, if you suck lightly on the tube there will be no flow as one of the flapper valves has closed. The cast tube has a metering jet pressed into ot and it must flow gasoline. I normally use a set of welding tip cleaners to gently ream out the metering jet. 2) While yo have things disassembled, you should replace the diaphragm in the carburetor. You can only do this when the carburetor off of the engine as the muffler is in the way. The diaphragm is inexpensive ($2 to $4) and widely available. 3) Lastly, while the carb and tank are off, I would check intake and exhaust valve clearances. The valve chamber is directly below the intake and exhaust ports and has a cover held by two screws. Proper clearance is .008 intake and .015 exhaust with the piston is 1/4" beyond TDC with both valves closed. Use a feeler gauge to measure. Usually exhaust clearance is OK because Briggs used relatively high quality steel. The intake, however, is little better than a nail and will stretch causing the valve to lose clearance. If clearance is OK, close up the tappet chamber and proceed to reassemble the engine. 4) If you have insufficient clearance in either valve, you will have to remove the cylinder head, and pull the valves out. Additional clearance is obtained by grinding the end of the valve stem. Remember, you can take metal off but not replace it. Grind slowly and measure often. Reinstall the valves, springs, and retainers, and remeasure with a feeler gauge to insure clearance is correct. Now you can reinstall the cylinder head, put the carb back on the tank, and reinstall on the engine. You should now be good to go.

A properly sharpened and set up reel mower will always give a better cut than a rotary. Reel mowers cut like a pair of scissors, the grass is cut by a moving blade against a stationary bedknife. It also gives more even results as the bedknife holds the blades up while they are cut as opposed to being hit by a spinning blade with some lift provided by a suction effect from the blade. After I cut my lawn with a rotary I usually have some missed blades. Reel mowers are the only ones that can cut very short, so if you want to have a fairway for a yard, then you need a reel mower. A bumpy yard however, will give an uneven cut at low heights (the yard will look even, but the grass on mounds will be shorter and in the dips will be longer), and scalping can occur, but this is also true of rotaries too. Rotaries, if their blades aren't very sharp will tear grass blades, so you get ragged edges, which isn't great for grass, although a poorly sharpened reel can have its issues too.

I think the first thing I would do is locate someone in your area that sharpens these. By me, the sharp service start around $80 and can cost a hundred or two more by the time you are ship shape.

I am personally more of a Trimmer fan, but respect Tru-Cut as a very good mower. Both have excellent reel and cutting bar assemblies, making them top of the class for St. Augustine, Bermuda and other crawling grasses which are kept low. I prefer Trimmer for the roller drive. The wheel drive of the Tru-Cut has a differential which sometimes loses traction on slippery surfaces like wet grass. On the other hand, because Tru-Cut has two clutches (drive and reel) you can move the mower from one location to another without spinning the reel. I suggest you try to operate both mowers and decide which is better for you. Good shop will usually have a test patch where you can try out their mowers. In either case, I suggest you stick to "C" or "P" model Tru-Cut, and the all chain "Original" Trimmer. Both manufacturers have "Homeowner" models which are slightly cheaper, but less competent. As for front wheels, I prefer fixed, and in the case of Tru-Cut, I use the feature which locks the casters in the forward position. An aftermarket supplier makes full width roller kits if you are into striping your lawn. I think they are $150 to $200. The Deere's, Toro's, and Jacobsen's are professional golf course machines. They are better for putting greens, but not what you want for a home lawn. They'll do the job but why spend $3K to $5K for no significant advantage in your application.