Your watch is a late Carrera 12 reference 2447 NT, which is row D-8 on our Carrera reference table:

http://www.onthedash.com/Guide/Master_Reference.php4

Here's a photo of another example:

It's great that it's still running and that you want to get it up and running still further. As to what to restore and repair, that's ultimately your decision; though some restorers might be keen on pushing you to go as far as possible towards getting everything pristine, I'm not convinced that's always the best way to go and that some patina and wear is worth taking in order to keep originality. That though is a personal decision and not the same for everyone.

Let's start with some of the non-controversial items:

- replace the missing lower pusher. These crop up sometimes on eBay etc and quite possibly some of the people on this forum would have one in stock.

- replace the hands if possible. I say replace rather than relume because these hands have either lost the black centre insert or are replacement hands; the seconds chrono hand definitely looks like a replacement as it seems to reach the outer edge of the internal 1/5 seconds ring rather than the inner edge. These hands are harder to find than the earlier plain hands but that insert is part of the look of the watch and they always look best with these. The existing hands could be tidied up while the search is on perhaps.

- replace or polish the plexiglass. If replacing, you might also be able to replace the internal 1/5 second ring for a cleaner one, though bear in mind you might not want to depending on how much the registers on the dial can be cleaned. Don't consider removing that ring entirely - these early Carreras always, always look better with even a dirty ring than none at all.

- service the movement. It looks a little dirty so some parts may need replacement, especially as the chronograph isn't functioning. Fortunately the Valjoux 72 is a well-known vintage watch movement and was well used by many major manufacturers in its time, so finding parts might not be as hard as for some other movements.

Now onto some of the points where some views may differ:

- reluming the dial. I have rarely seen this done well - on these early Carreras, this involves removing the hour markers so that part of the lume's radius lies underneath the marker. Typically, the relumer does not go to that effort and you end up with a blob of lume sitting on or by the marker, which doesn't look right and is by no means original. An easy decision for me - it's quite common for lume to have degraded and gone in a vintage watch, so I am happy to leave it at that but I know some people disagree.

- polishing the case. Cleaning definitely, I don't think anyone would have a problem with that. I'm a believer in letting a watch wear its scars of age; others advocate polishing. If you go the polishing route, then ensure the polisher will leave references intact and maintain the iconic sharp edges of this Carrera case. Looking at the watch, the case seems in good condition and not in need of a polish to me, but that's one for you to decide.

- redial. Possibly the most controversial of all. I have rarely seen this done at all well. Ideally, you could find a replacement dial in good condition and use that, I don't think there would be any controversy in going that route. Let's assume that you won't be that lucky, though, and we need to do something with the existing dial. I'm kind of torn here myself. I really value originality but the white text on these early black Carreras is very prone to breaking up, as on this example. It has been retouched on a lot of watches but to me it then never looks quite right. So the decision is then between complete text that might not like quite right or the current broken, but original, Heuer Carrera text. Tricky one. If it was me, I would see if I could look at the watch with the rest of the work done, then decide on whether to have this retouched - once that's done, you can't go back of course. The Tachy scale doesn't look too bad - 150 looks totally obscured, 160 partially, as are 750, 500 and 80 (as far as I can tell from the small photos). I'd be tempted to leave that as is. The rest of the dial can be cleaned without redialling and see how well that comes up before making a decision whether indices etc would need to be repainted. If the watch were mine, I would have the dial cleaned but not redone and would remain on the lookout for a replacement dial thereafter.

So a fair amount of work, but the watch is worth it. I've not had a watch restored to that extent, so can't suggest someone for you - there are some on the forum who could do the work but I'll leave them to come forward if they want to take it on. Failing that, I'm sure someone will be able to give you a contact, either in the UK or continental Europe.

Good luck in getting it restored and when it is, please treat us to some before and after photos - I'm a sucker for those!