The short answer: the model designation has nothing to do with the engine. You probably see more L models with HG replacements simply because they sold more of those than the S model. Here's a handy site to explain the differences:
http://http://www.cars101.com/subaru/forester/forester2002.html
At the mileage on the '02 in question it would be time for the timing belt/water pump/front seals replacement. If you're going to do HG's, now is the time to get it done. Half of the timing belt job has to be done with the HG's anyway. Look at it this way: if you spend the money and do it now, you're DONE. No worries for another 100k easy. Unless you can find a Foz with a service history showing this stuff has already been done, it's going to be an issue with any that you look at.
Your Impreza comes from the bullet-proof years when hardly anything went wrong with them. We had a '96 Impreza that went to 217k before we sold it. The 2.5 HG issue is an expensive one, but it's really still about the only serious thing that goes wrong on these. I took the risk and bought one like yours and wound up having to get the HG's replaced, but to me it was still worth it. No other vehicle could do what the Foz does without being a Stupid Urban Vehicle that drives like a truck. You can read about our purchase and philosophy here: Foz
http://http://www.cars101.com/subaru/forester/forester2002.html
At the mileage on the '02 in question it would be time for the timing belt/water pump/front seals replacement. If you're going to do HG's, now is the time to get it done. Half of the timing belt job has to be done with the HG's anyway. Look at it this way: if you spend the money and do it now, you're DONE. No worries for another 100k easy. Unless you can find a Foz with a service history showing this stuff has already been done, it's going to be an issue with any that you look at.
Your Impreza comes from the bullet-proof years when hardly anything went wrong with them. We had a '96 Impreza that went to 217k before we sold it. The 2.5 HG issue is an expensive one, but it's really still about the only serious thing that goes wrong on these. I took the risk and bought one like yours and wound up having to get the HG's replaced, but to me it was still worth it. No other vehicle could do what the Foz does without being a Stupid Urban Vehicle that drives like a truck. You can read about our purchase and philosophy here: Foz