You can feel the boost best in 2nd gear as you hit over 2.5k revs you start to feel it pull more and just want to keep going.
As for turbos, you have a k03 not a k03s, easiest way to if its a genuine KKK turbo is it will have a blue tag with the part number on the side, no blue tag avoid at all costs as it will be made from chocolate, some fakes use a deep navy and black tag, avoid them too. As you said you have seen allot of cheap new unit on eBay for £200, they don't have the tags or have different colored tags as they are replica's and avoid at all costs. The tag should look like this:
As for turbos anything that ends in -011 to -049 is a ko3, whilst k03s are:
k03-052
k03-053
k03-058
Only difference for the k03s is the TIP fixtures slightly different at the bottom, but if you uprate the TIP with a silicone version (such as forge, or demon) it will fit with no issues on the AGU.
Like you said, cats are not much of an issue and you can pick them easily off eBay.
As for the to rebuild or 2nd hand turbo business that's your choice? But how many miles has your turbo done? If it's like mine and only 89k 2nd hand can be hard to contemplate as you will be buying a unit with similar mileage that's due to go out soon like yours just did, it's a lottery. It also depends how long you plan to keep the car, if only like 20k more miles then 2nd hand might be the best option. Otherwise head for the rebuild route or try and find a turbo 2nd hand with less miles on it such as 50k, 60k and so on....
I got mine from ebay.de, was abit hard to sort out payment information as it was my first time with dealing with overseas banking, plus the language barrier, but after 3 days it was all sorted and payed for, here's some turbos on ebay.de incase you want to give them a go:
k03:
http://cgi.ebay.de/Audi-A3-VW-Golf-1-8T-Motor-K03-Turbolader-AGU-ARZ_W0QQitemZ220554756180QQcmdZViewItemQQptZAutoteile_Zubeh%C3%B6r?hash=item335a168054k03s:
http://cgi.ebay.de/Turbolader-Golf-GTI-Audi-1-8-Turbo-180PS-AUQ-AJQ-K03-TT_W0QQitemZ130364782348QQcmdZViewItemQQptZAutoteile_Zubeh%C3%B6r?hash=item1e5a58b70cIt's all your choice, I'd personally base my evaluation on how many miles your turbo has done whether 2nd hand is really cheaper or whether you got for a rebuild. There's also Max's offer their.