Options for carrying a smart briefcase on a bike (pannier or otherwise) Situation

I don't own a bike: however due to a recent change of office location, I have worked out that I could cycle in half the time as driving through rush-hour traffic every day. I'm therefore interested in the idea of purchasing a bike

Issue

I carry a smart laptop-size briefcase to work, which is just fine while driving - however I need to figure out how I would take it on a bike, if I choose to buy one. The briefcase is approximately 45cm long, 30cm high and 12cm deep. It looks similar to this one:


What I've thought of

I'm aware that luggage is normally taken on bikes by means of panniers. However it seems to me that directly attaching such a bag to a pannier rack by use of "spiders" (bungee cords) would be fairly unstable. The problem is that the pannier racks I have seen are usually pretty narrow (only just wider than the rear wheel); and therefore there isn't much of a stable "base" on which to place such a bag. The bag would have to lie flat - but also due to the limited length of a pannier rack, it wouldn't support the length of the bag - meaning that the bag would have to sit length-to-width. I.e the length of the bag would sit from left to right across the top of the rear wheel, only supported by a relatively narrow pannier rack in the middle. I can imagine that this would be fairly unstable.

From what I see, pannier racks are intended for especially-designed bags to be able to clip onto their sides - hanging down beside the wheel. However what does one do when one has an existing bag like the one above, which would not fit into one of those soft-sided pannier bags?

Does there exist some kind of pannier clip, or cage, which could attach to or contain my bag, to enable it to clip properly onto the side of a pannier rack?

Does any other solution exist which I have not considered?

It may be pertinent to note that my eye is on a folding bike - as I only have a small space in my shed, and nowhere to store a full-size, non-folding bike. Therefore any solution involving somehow mounting a cage within the frame under the crossbar would be impractical.

Any suggestions or advice appreciated
Depending on the thickness of your briefcase it may be a solution to hang it under the frame in the main triangle (if it fits there) but since you are thinking about a folding bike it is not a solution.

I've seen something else couple of times - a special carrier for briefcases:

 

I'm not sure how a folding bike would accommodate such a carrier as it attaches to the seat-stay and the back of the normal rear rack.



Another idea would be to put the front baggage rack and tie the bag there. Not only is this more stable (the bag is "in your hands") but you also have the bag (probably containing important documents) always in sight.

This is what I mean:

But again - folding bike limits your possibilities.