Replacing Chain and Cassette with lower and higher gearing
I am looking at replacing my chain and cassette as they are both worn (3k miles on both) I have a 2001 Cannondale R600 tripple caad4.
I am looking to increase my hill climbing ability when loaded (rear panniers and trunk) my current weight is 225# and there are a few hills I climb that leave me sounding like a steam engine, but end up really mashing up the top parts, talking 12 to 15% grades for a half mile or so (look vertical on elevation maps).
Any way here is my current config: cassette -- Shimano Tiagra 9-speed, 12-25, Rear Dérailleur -- Shimano 105, chain rings -- 30/42/52
You actually don't need a longer chain. That new set-up looks good, will give you one lower gear to use on those climbs. You might also want to look at getting a 28t granny gear as well since those wear out quickly.
You don't say which cassette. The Shimano 105 rear derailer probably won't run on the 11-34 as it is limited to around 28 or 30T cogs. You would need an MTB (aka alpine) rear derailer, such as a Deore, to use that cassette.