I'm looking at getting a remap to 156bhp in some months time (over 20% increase means my insurance goes up a big increment).

Reading around the forum, people are talking new clutches/ fly wheels/ turbos/ exhausts/ intakes etc.

For 156BHP, what must I realistically do to keep my Furby healthy and intact after this increase, and in what order?

For 156bhp - Do absolutely nothing

Some stock Fabias are pushing out that kind of power so i really wouldnt bother. I've got 173 and (touching a lot of wood) all standard components are doing just fine. I would however invest in a more free flowing panel air filter such as Green or K&N (roughly £35)

I'm probably about to incite some kind of riot here, but would an insurance company really notice if you remapped to 170 but told them it was 20%? With stock Fabias being underestimated anyway, technically it would be true.

For a 'sensible' amount of power you dont need to change anything in particular other than the remap.

Exhaust - waste of time generally although it looks nice® I guess and if you go for straight pipe there is lower EGT, however that's not really that much of a factor IMHO with the power levels you're looking for.

Flywheel/clutch - the DMF will strugle if you boot it from low revs. Ditto for clutch.

If you drive with some sense you can use a reasonable amount of the power/torque without it causing problems, when higher up the rev range the remap will make the car much nicer to drive and it will pull till the red or somewhere near it if desired.

Heatsoak could become an issue as it is with the standard map during hot days. However the cheap option is to do the arch venting (pikey mod I and II) mods, which is not an engine modification (so saves on insurance outlay possibly) and you can do it yourself (so cheap )

For most remaps, a PD160 air intake is recommended. Mainly so you get more air into the system so less likely to smoke like crazy. However the part has got significantly upped in price by seat (VAG in general) due to demand.. Basically try to buy second hand if you get lucky, or you may have to swallow the cost.

It is worth considering handling upgrades too, if you use the power a lot you may find the car wanting for better road manners, as the standard suspension isnt all that great, it's decent but not that grippy etc.

If you have a tuner who you can ask for what you want, and you get a smooth map with not too high a torque spike low down, the clutch should last a lot longer.

Turbo - no point, 170ish bhp is still fairly safe, higher than that is pushing the turbo hard and although it works, it can go.

Filter wise - green filter is worth considering, or replace the paper one every 10k, it does NOT last 40k without seriously clogging up. They are quite cheap, and it's a reasonable alternative.

^ a nicely amplified version of my answer