Random daydreaming: cheapest Turbo/SC engines for ill advised swaps...

Since turbocharged engines explode (or just overheat and blow head gaskets) with depressing frequency in Lemons, engine cost and junkyard availability should be at the top of your list. I think the best approach might be to find a very common/cheap engine and then ghettocharge it using Eyesore Racing's techniques and a junkyard-common turbocharger.

Rust in the Wind has had good life expectancy with their Saab Red Top from a 9000 series.  In the NorthEast their are tons of these or at least their used to be. 

240 hp with their best Saab 2.0L Turbo add a few trick parts and 300 is easy but as Phil mentioned their reliabilty goes down hill as you mod them.

GM 4 cyl Ecotec is an option, they are cheap and plentiful from all manner of GM related vehicles from 2004 to the present day. I payed $84 at pick and pull for a 2.2 Ecotec out of a 2004 Cavalier on half price day. HP ranges from 150 to 250 if you step up to a 2.4 and there are plenty of factory turbo and supercharger options. The supercharges from cobalts are a bit spendy for Lemons but the turbo setup on a 2.0 Saab (also a GM ecotech block) will bolt on without much drama and the internet fanboys say you can easily push 300 hp in a standard engine. These are reasonably well designed, all aluminum engines that can be had for Lemons money all day long.

Most are FWD but the Pontiac Solstice/Saturn Sky used these engines in a RWD config so there are bellhousings available for the AR-5 transmission also found in Chevy Colorado. There are also Ecotech to T5 aftermarket bellhousings available.

Some of the Jeep bellhousings bolt up to W series Toyota transmissions and a W58 is a nice strong trans....

The original list is good. I'd add the Mazda B-family of engines; the fairly rare B6T was in the Mercury Capri XR2 and made 130 horsepower, but the general word is that the stock internals of the normally aspirated B-series engines (obtainable in various forms the Miata, the Escort GT, a whole bunch of cars...see the link) can take a healthy dose of boost from a non-original TRUBO. From what I can tell (mostly based on Eyesore's experiences), running 175 horsepower or so with that engine gives a pretty solid mix of power and efficiency.

Whatever turbos they put in the Saabs seem to be reliable enough of their own accord; might be worth looking into.

From Wikipedia describing the SAAb turbo version of the GM Ecotec.

"LK9 is a turbocharged 2.0 L— 1,998 cc (121.9 cu in)—version of the L850 (86 mm bore) series ECOTEC utilizing an all new reinforced sand cast aluminum cylinder head and reinforced internal components. This version of the engine also has Saab's Direct Ignition system and in Saab vehicles features Saab's Trionic 8 engine management system as well as a revised valve train. The timing chain and timing gears are also new. The reinforcements, turbocharging, internals and such were developed by GM Powertrain Sweden. It features an 86 millimetres (3.4 in) bore and stroke and a 9.5:1 compression ratio. Power is 210 horsepower (160 kW) at 5300 rpm and 221 lb·ft (300 N·m) of torque at 2500 rpm. Maximum boost is 12.3 psi (0.85 bar)."

That is all well and good but the Turbo exhaust manifold will bolt onto any 2.2 or 2.4 ecotec and the basic block is the same these are cheaper and more plentiful in junkyards.
I have both sitting side by side in my garage right now

It should be like the K-Car's original engine but faster. And by "faster," I mean how "the pace at which it created engine externals."

Poor Mitsu 4G63T. Gets no respect these days. Earlier (90-94) 6-bolt crank is the one you want. Transverse and kinda tall, but very strong bottom end and 250hp doesn't bother it. Just needs lots cooling and good oil supply.

Not the cheapest or most reliable choice, but you can make gobs of power and would have plenty of aftermarket support.

A friend of mine had one swapped into a '91 BMW 318i. Not sure but almost certain he used the BMW transmission. Also pretty sure the 4G64 (2.4 NA) was mounted longitudinally in the old Mighty Max pickup trucks.

<slight threadjack>

. . . I see what you did there. . . .  brilliant!

But here's whatcha oughta do if you're really into the 'ill-advised swaps':   I know there's a trophy in there somewhere!

You need two cars for the swap, right?  One donor, one donee?

But then you have an extra shell, and an extra engine, right?  And the job's only half done; you have to clean up the yard anyway, so:

1.  Buy turbocharged Saab .
2.  Buy turbocharged Volvo.
3.  Put Saab engine in Volvo.
4.  Put Volvo engine in Saab.
5.. (optional) Call yourselves the 'Swedish Transplants' for extra thematic points. ..
6.  DOMINATE!!!!