Try not to read this on a phone!
If you are not good with Inboards and Stern Drive's it certainly can be a bit daunting and I know exactly where you are with this. Even if you are ok with them, there are always hidden bits and pieces which can catch you out.
Agree 100% with James, a Service History is your first step and BB has given some good tips too.
Main dealer servicing is good but you also get the anally retentive owners who has over serviced it, i.e. impeller changed every year without fail, even though that is in the schedule. These are the sort of things you'll find out if you are able to talk to the owner.
I suspect you'll get either,
1/ Owner who knows nothing mechanically but likes to be safe......I know nothing about engines I leave it to my engineer, in which case they'll be records of invoices etc.,
or 2/ Anally Retentive .....You'll get a never ending list of all the things he/she found wrong with it in the first place and how it was fixed and what they did over the last Winter, down to the choice between Synthetic and Semi Synthetic oil in this year of engine etc. etc., or finally you might get,
3/ The one to get an Engineer in to look it over...... Yes it has been serviced in 2013, "what sort of service?" I don't know my mate did it! No invoices or paperwork!!

Also be careful to ask questions if someone says its been fully overhauled, this gets bandied around a lot, then you find it hasn't had exhausts changed.
Most older boats sold, will need something doing in the first year. The sort of engines you're looking at are either a V6 4.3 or a V8 5.0 or 5.7 it's important to know which are the expensive items to replace. Apart from establishing Service History, which I guess at this stage you have now done, look for records of Winterising. These engines are raw water cooled and if they haven't had anti freeze added during the Winterization process, during cold snaps water without anti freeze left in the engine can crack the block. Most of the time, if this has happened, it shows up with bad running on the sea trial.
Next to look at would be the Exhausts, Risers (not all engines have Risers, small blocks between manifolds and elbows) and Elbows. Depending on Fresh or Salt water these can last between 5-10yrs and longer in some cases. Costs vary but about £1k would cover most types and OM parts even more. Fitting is fairly simple if you have enough space but I'm guessing £5-800 ish from a marine mechanic. If these fail water will run back into the cylinders with catastrophic effect. As you can't see inside these, you might ask how you know if they are OK. Water flow is a good test, with the engine running if you can put your hand on top of the elbows and its hot, that's fine, if you can’t touch them, then they may be blocked. Also, if the owner has had the boat a few years and not changed them and they look old and rusty, that's a sign they may require replacement.
Moving to the stern there is a Transom Shield on the inside which takes the exhaust and various cables to the water, check for leaks here, in the bilges etc. The Shield is bolted to the Gimbal Housing which is on the outside, which holds the Stern Drive. Check the drive for looseness, it might move about a bit from side to side but shouldn't move up and down. If it does wriggle a bit have someone in the boat to check if it is only the tiller pin a bit loose, anything else in the Housing area can be expensive.
There are Bellows inside the housing, two of them are important, Drive Bellows (the big one) and Shift Bellows, very small, if these leak, worst case, they could sink the boat, not so bad but expensive, damage the Drive Shaft and Gimbal Housing and in the case of the shift bellows leak into the boat and replace the cable. The 3rd is the exhaust bellows if this leaks it will only make a noise, but when changing them it is usual to do this one as well. The Drive Bellows basically keeps the drive shaft and Gimbal bearing dry and the Shift Bellows covers the Gear Shift Cable and acts like a seal where the cable goes through the Transom. By the way, Stern Drives stored with the leg up can be prone to stretching the bellows shortening their life, but if the boat is on dry land lifting the leg to the trailering position, fully up, gives you a bit more room to inspect them and take a torch as well.
Drive oil is a good indication for a leaking seal in the drive. As BB said, later boats have a header bottle to top up drive oil, emulsiphied oil will show as milky. If it doesn’t have the bottle, the only way to check the gear oil is to let some out and look at it. Taking Stern Drives apart can be expensive. If the boat is in the water a film of oil on the surface next to the drive is also an indication that a seal may be leaking.
Impeller and Impeller housing changes should have already been covered with history checks.
Lastly if it cannot be checked if the Drive has never been off, getting it out can be a real pain. Drive could be rusted in the engine, Gimbal Bearing (Oh that’s a bearing about 10cm which sits in a case in the Housing and supports the Drive shaft through the transom). If you take a sea trial, any grumbling noise from the stern whilst running indicates either a worn Gimbal Bearing or Drive UJ’s. By turning the steering to full lock both ways the noise will increase if it is the Gimbal Bearing. Not expensive if you do it yourself but a few hundred quid by a mechanic.
Pictures are always a help too.
Hope this helps a bit.