As above, definitely go with an ICE specialist, not a discount store:
1. door speaker wiring: several options here, but because of the multi-pin plugs in the door jams, it's not easy to pass new wire; it is fine to tap into the factory speakerwire inside the cabin either in the kickpanel areas (ie: locate wires in looms before they leave the kickpanels into the front doors) or from behind the headunit (ie: the speakerwire ISO plug); the latter is easiest by far (= cheapest in terms of labour costs), but relies on the full length of factory speakerwire; mind you, I say this is perfectly adequate for what you are wanting (ie: anything less than a competition system)
2. speaker size: the factory speakers fit into the door trims/cards, which are moulded accordingly; but it means if you want a true drop-in replacement, your choice will be very limited because they only accommodate speakers with a small frame/magnet; better to modify the fitment by slightly trimming the plastic to open up the hole; better-still, enlarge the hole considerably, and mount a new wooden spacer ring directly onto the door for the new speakers, which can then accommodate virtually any on the market; I wouldn't allow a discount store installater do this work
And as above, new powerwire (fused) from battery to the amp, which will presumably go into the boot. Amp mounted and 'isolated' on a wooden board, mounted securely.
I wouldn't tackle this job if you've never installed a stereo like this before. But you can learn from what is done, and attempt stuff in the future.