How can I replicate an integrated double oven and cooktop unit with individual components?
Top - Microwave
Just look for built in microwave and you should find plenty. The catch is that a built in microwave generally costs a lot more than a countertop microwave. The advantages are that (a) they are (in my opinion) generally built to be more durable (i.e., replacement parts available instead of &quot;toss it when anything goes bad&quot;) and (b) they typically include a light &amp; fan below as they are designed to be used over a cooktop.
You need to check the installation guide for the microwave oven to figure out how to mount it, as it will need to attach directly to the wall (into the studs - don't rely on little anchors or toggle bolts for this!) or to an upper cabinet.
Middle/Bottom - Separate
A separate gas cooktop for the middle and electric oven for the bottom.
The electric oven would really be a &quot;wall oven&quot; but installed in a lower cabinet instead of higher up in a cabinet/wall. However, you will then need cabinets built to hold them. While in the old days a cooktop (gas or electric) would have a false drawer front (like for a sink), with modern cooktops you can often use a regular drawer with a cutout for the gas pipe and/or electric cord (gas cooktops need power for electronic ignition). This has the advantage of easily (i.e., relatively cheaply) getting a gas cooktop together with an electric oven, which many people (myself included prefer) as gas provides better control for a cooktop than electric while electric ovens often work better in a number of ways than gas ovens.
Middle/Bottom - Together
A slide-in, standard width combination cooktop/oven.
This is the easiest solution, and often the cheapest, but does not provide as much flexibility. Similar to your old Tappan, except without the top oven. If you want to have gas cooktop with electric oven, your choices are relatively limited. Most manufacturers, at least on the low-to-mid price range, use the same heating method for cooktop &amp; oven.
Power!
Your existing Tappan most likely had a single gas connection and a single electrical connection. If both ovens were gas, then the electric connection was most likely 120V, possibly just 15A or 20A as it only needed to power the clock, controls and electric ignitors but not provide any heat. If one or both ovens were electric then you probably have a 240V, 40A or 50A connection.
For a new setup, you will need:

Gas for the cooktop (and possibly oven, in which case it would be one connection)
120V, 15A or 20A (check the specs) for the top microwave

One of:

120V, 15A for the cooktop ignition, plus
240V, 40A or 50A (check the specs) for the electric oven

or

240V, 40A or 50A (check the specs) for a combination gas cooktop/electric oven

or

120V, 15A for ignition and controls for a combination gas cooktop/gas oven

That means, at an absolute minimum, you will need an additional circuit for the microwave oven. But you may also need a new and/or upgraded circuit for the bottom oven, depending on the type of appliances you choose and the existing wiring.
You will also need to paint and/or tile the space between the cooktop and the microwave oven as there won't be a metal backsplash in between like your Tappan has. You may find the wall behind looks great, or the builder may have left it as unfinished drywall because &quot;who will ever know&quot;.
There are really a lot of options. If you stick with the same brand/style, you can actually get a very nice match between the 2 or 3 appliances, or you can use different brands and if they are all stainless steel or all white or all black then it will generally look pretty good.