Frankly, I think that Civic at $10,000 +/- is a great deal. The fluids look "normal" to me for the use that the car sees. I think Honda transmission issues are severely over-hyped, as most issues are on the internet. Consumer Reports indicates excellent transmission reliability in the Civic for close to a decade now; I'd wager that a good number of Civic owners are also CR subscribers, so I imagine that if there are trouble with Civic transmissions, it'd be showing up. In fact, the '08 shows full red circles for every category; as pretty much everybody knows, a used Civic will be generally a low-risk purchase.
Regarding the semi-hard starting, is it possible the battery is getting weak? I don't think Hondas are generally known for long-lasting batteries. If the battery is original at this point, it may be getting weak. I replaced the original battery on my '08 CR-V last month, and it has 48,000 miles on it. Our '05 Acura is on its second replacement battery now.
That Civic may need plugs at this point, and could use a re-new on all the fluids. All-in, I think 10 grand for an '08 Civic is a pretty square deal, especially when you pretty much know the history on it. I'm sure you can find other cars out there for less money, but I'm not sure you'll substantially lower your risk, which you have with any car purchase, new or used.
It's easy for me to spend your money, but if she likes how it rides and drives, and you're mostly confident you can TLC-it back into new condition, I'd pull the trigger on it.
