If you are buying an outboard privately, then the first thing to do is check proof of ownership, so that's paperwork and receipts and plenty of them. The serial number will also age the outboard. An hour meter is also a useful guide, but don't rely on that 100%.
Next on to the general running of the engine. Always buy after you've seen it running. And where possible check its started from cold. There are things you can check yourself such as tell-tale stream strength, smooth idle, vibration, compression on all cylinders within factory specification, etc. I'd also pull the plugs - this can highlight a multitude of problems. Plugs should be dry, with almost a light copper dusting on the electrode. Also check out the propeller for any signs of damage, the skeg, and sacrificial anodes are doing their job.
If its been serviced, then all well and good, if not, then budget for a new water-pump impeller, new sparks, gear oil, thermostat, etc. Not sure about ETECs (need specific spark plug installation procedure called indexing), but I'd be expecting £200+ unless you're any good with spanners and can DIY. This is a useful guide on ETEC spark installation. Spark Plug Indexing – How To | Evinrude Nation Community
Other things to look at is the trim and tilt. It should go up and down smoothly. Check for any signs of hydraulic fluid weep. An intermittent or noisy trim could be a sign the trim motor is failing (worn carbon brushes), dodgy electrics, low hydraulic fluid, etc.
On the subject of electrics, then check the condition of the loom itself. The remote control and wiring loom are expensive to repair or replace. Special interest should be made to areas with more insulation tape than you can shake a stick at!
Check the condition of the battery. Should be sitting at 12.7 volts before cranking. If it needs replaced then you're looking at at least another £100+. If the battery isn't maintenance free and can be inspected, then check the battery acid level. You can top up with de-ionised water. You can also charge before trips. A cheap multimeter is a really useful tool for checking battery condition, isolating and pinpointing electric faults, etc.