Howdo Hedge, I've had a Mk2, 3 and 4 Mondeo and a couple of Mk4-5 Escorts and I'm a bit of a Ford fan so bare that potential "bias" in mind with the following -
The Mk4 is a nice successor to the Mk3, with the same reliable (if driven right) engines but a much better step-up in interior and with, to my eyes, a much better exterior too. They still drive and "feel" just like a solid Mondeo and the engines/chassis are well enough known by now that any major flaws are well documented (there's not much wrong with them TBH) but, as with any modern diesel, if you're doing only "town" miles the EGR system will still cause problems unless you can get it out for a long blast regularly to clear everything.
My last Mk4 was a 200k+ mile 2.0L ZETEC TDCI which was being sold cheap due to the high motorway mileage at just £2k and it still felt nice and tight to drive with a very reliable engine (doing 20k a year commuting). With a few little "tweaks" like a new Android headunit from eBay with Sat Nav, reverse cam, DAB etc to replace the fairly basic (but top of the range) OEM Sony unit and a BlueFin remap it made the car even better. Eventually I traded it in after around 2 years to get my 2nd RS6.
In the 40k miles and 2 years I owned it all that needed doing was a replacement passenger headlight which leaked water into it quite badly and a blocked pollen filter (git to change) which gave the symptoms of a dying fan (only blew air on full speed). Both were cheap fixes and nothing else broke, although I may have just been lucky!
For the £3-4k budget you'll have no problems getting a sorted one if you decide to move up rather than fix the Mk3. Speaking of which, when I had my Mk3 TDCI with 2 semi-failed injectors it would struggle starting with a puffs of blue smoke then after 5 seconds 1 injector would "work" and then after another 10 seconds the 4th one would work too and the car drove fine but the MPG was always awful as the injectors were badly leaking. It cost around £150 per injector to replace and recode the new Delphi ones IIRC. That one also got traded for my first RS6 too