I just bought a two Simano Exage travel rods, along with two Shimano fixed spool reels to take on holiday. See link below (these were the best prices I found, although my local tackle dealer matched the prices so I bought them locally)
http://www.wickfordangling.co.uk/shimano-sp/exage_spinning_rod.htm
I got the TEXS240M 8' (10-30 gram) and the TEXS330H 11' (20-50 gram). I also got the Exage 4000FA reel, and a Nexave 4000RA reel to use with them.
I tried out the 10-30 gram 8' rod last week, and am very impressed with it. It will no doubt be the rod I will be using for all my light spinning work at home, as well as fitting in my suitcase for holidays. I am hoping that the bigger rod will also impress me as much for other spinning tasks. The longer rod fits into my suitcase but only just so be aware of that. The smaller one easily fits in a suitcase. Both rods can be made 1' shorter by swapping out a section.
I opted for the take apart versions as I am unsure of the robustness of the telescopic ones.
Anyway, back to topic. I think you will find that these compact rods will easily do the job of all of your spinning - but with the added advantage of being able to stay in your car for impromptu sessions when the urge takes you, and can go anywhere with you.
There is also a post somewhere on here about the Shimano Beastmaster spinning rods that a couple of the guys seemed really happy with, but they are a little dearer.
You can get the Exage 4000 sized reel for about £47, and the Nexave 4000 size reel for about £33. (The Exage reel has fancier bearings I think)
In summary, for your £100 budget, I think you will find the above options very versatile.