lol, didn't mean any offence, just the way I type...
But yeah, facts can be kinda handy
Anyhow.
Stock Series axles are weak, but for most 'normal' Land Rover use are ok. Not many upgrades for them, you can change the crown wheel and pinion, but pretty much stuck with half shafts and the rest of the setup.
Coil axles from a Defender/Discovery1/Classic Range Rover aren't massively different. The 3.54:1 diff is stronger (as in the crown wheel and pinion) and so are the half shafts. The diffs are interchangeable from a Series to a coiler axle, but a Series is 4.7:1 ratio, so you need to consider the affect on gearing.
Stock coil axles n grand scheme of things are not that strong either. However, for normal tyres sizes and normal off road use, they should be fine. So running say up to a 32" tall tyre. Occasionally a half shaft, CV or crown wheel & pinion will break, but usually cheap and easy to replace and repair.
If you want to spend some money on the axles, then there are upgrade options. Not sure in your part of the world what is on offer, in the UK, Ashcroft Transmissions are the go to place, but there are others. You can get stronger crown wheel and pinions. Different ratios and stronger half shafts. You can beef them up to cope with 35" tyres and a fair amount of abuse.
If you want bigger tyres still and still abuse them, then you'll have to consider a complete axle swap.
Pro's of sticking with the Rover axles.
Well it keeps it all Rover.
So things like props, hubs, wheel rims, etc fit.
Con's.
Coil axles will be wider, so will increase the vehicle track. This isn't a bad thing, but will make the wheels stick out of the arches (not legal in the UK). So you'll normally have to fit Defender style wheel arch spats or something similar. And you sort of lose the "Series" look of the vehicle.
You'll need to fabricate the perches for the leaf springs. Not a big job, but sometimes requires a little thought. But this means some welding will be needed and they aren't a bolt on.
There are lots of other axles to consider however. Many people have fitted Toyota axles, Ford axles, Dana axles and even Mercedes Unimog axles. But all will require more work and more cost.
Remember on a Series the gearbox is also a potential weak point. And as the gearbox mates to the transfer box, any gearbox swap will likely involve swapping out the transfer box too.
You can go LT-77/R380 5 speed box and a LT-230 transfer box. Lots of people have. But on an 88 can make for a very short rear prop and will require some custom parts.
But the world really is your oyster and anything is possible with time and money.
This place sells lots of interesting adapter kits for different engines and transmissions for Land Rover products:
http://www.marks4wd.com/engine-conversions.html
Personally I'd keep it simple. A good Tdi or a 3.5/3.9 Rover V8 in a Series should be fine and offer a good performance hike. A Tdi will be noisy and unrefined, but better on fuel than a V8 and an easier conversion. You won't need to upgrade the gearbox or axles to get it running.
Once running, see how it goes. If you keep breaking stuff, then upgrade those parts.