For ease of installation, and being relatively inexpensive, a 901 is the best choice in my opinion. A 915 installed would require more modification to the car, and a Hewland transaxle would cost way to much for civilian use. The LSD in anything will add the price you've expected to any option, unless you just luck up on finding one in the 5 speed you choose. A berg 5 conversion will likely cost more than a LSD for any Porsche transaxle.
You won't be using any of an early 914's linkages, so the sloppiness associated with them will not be an issue. Most of the linkage parts you'll need for a conversion is from a Type I, with the exceptions of the coupler to connect the shift rod to the gearbox which is needed from a 911, and the shifter itself coming from a 914, or early 911 because of the wider gate for a three rail shift pattern.
I consider the shifting quality in mine to be on par with a stock Beetle. I haven't missed shifts, or had to row at the shifter to get into the next gear. It always feels positive, and easy to use. The shift pattern takes getting used to. I've never had a car with a dogleg shift pattern before.
Theres a technical article in this site, and some print articles from magazines floating around outlining the installation in a Beetle. Doing the same in a 181 shouldn't be much different.