I did encounter an idiot or two during the drive through Taroko and up the mountain, but you just have to be a bit careful and let them pass whenever the road is wide enough.
Can't remember exactly as my friend arranged the car but it was reasonable, I think 2600 Taiwan Dollar a day for a new Toyota Camry (though I wouldn't swear to it)Cheap or expensive (although compared to the UK everywhere is cheap!).
You can hire a taxi with driver for the day to see Taroko for around TWD 2500. I found public transport in Taiwan excellent - the HSR on the west side, the normal trains on the east side, as well as the buses are all good and easy to use, even with no Chinese skills.
Thanks again for all of the input, I opted to book for nine nights starting and ending in Taipei and am hoping to see a couple of other cities and spend a couple of nights on the East coast. Decided against staying an extra few nights as I wanted to cut the costs a little as I have my main holiday with my wife the week after.
if you are physically fit, highly recommend to get a bicycle and bike around the whole island. you can do it in 3 days if all u do is biking everyday.
maybe rent out a moped in taipei, then go around the island with it. it will be awesome.
Thanks Kale, the thought of doing a bike ride around the island does sound quite appealing but I find cycling for longer than 20 mins very uncomfortable as I suffered a dislocated knee a few years ago playing football and it never quite recovered. I'll consider the moped though the stories I have heard about the other drivers on the road does concern me.
Public transport in Taiwan is great - the HST and normal trains have English signage, while I found bus staff to be very helpful when there is no English signage.
moped will work a lot better for you, since we did 1200km. if you like scenic, you will like the east side where you have the pacific view from kenting to taipei. the road between su-ao and hualien was the most beautiful and amazing. if you remember the news back months ago where a chinese tour bus with tourists from mainland went missing, it was between on this road. doing it on a moped will be fine.
i saw a group of american doing the tour on mopeds. there are 7-11 and family mart EVERYWHERE in taiwan. the best thing about them if they always have an ATM inside.
a lot of the roads actually have a designated lane next to the slowest lane for bikes/bicycles unless it is 1 road with 2 ways traffic.