Replacing 11-32 Cassette on Touring Bike

+1 for new cables. It'll feel like dura ace in comparison.

£11 - 32 105 (5700) casette is available for £18.50.

I would only consider a 25 if
A) I was a pro
B) I lived in East anglia or Holland
C) my chainset was a triple (30/39/54)

My shifting improved no end when I skooshed all the moving bits with thin oil and also skooshed the bit under the bottom bracket where the cables run exposed over plastic runners. 

Chain / cassette wear usually causes jumping or noisy shifts rather than very lethargic shifts. Your symptoms sound like dirt in the rear gear cable loop (very common). Replacing this is not that same as fitting a chain or cassette. Did the shop not replace the cables when they serviced it?

KMC X10-93 chains are cheap and very good (ebay link - a reliable seller) but it's worth getting a chain checker or use a steel rule to measure the distance between 12 links (24 pins) when placed under load. A new chain should be 30.48 cm or exactly 12". When it is longer than 30.7 cm or 0.75 % wear it's time for a new chain. If you change the chain early enough your cassette will last longer.

To fit a cassette you'll need a chain whip and cassette tool, a good investment IME. Instructions at https://www.youtube.com/watch?v=05WxxDo4CvY

Replacing cables isn't difficult either - you need an inner, some outer and some good pliers or cable cutters. Note that gear and brake wires (and their respective outers) are not the same.

Just be aware that assuming you are planning on swapping these yourself, you'll likely end up buying a Shimano cassete tool and a chain breaker as well.  I've the Park versions of both which are great albeit I'm sure there are much cheaper options.

I've swapped the chain on my 2012 Tiagra 10spd setup a few times now, it's a 10 minute job with the right tools.  With a decent TLC routine I get 2-3000km out of a chain - I've not worn out a cassette yet - though I did buy a new 105 10 spd cassette when I bought some upgraded wheels for that bike - so both cassettes have about 5000km on them by now.

Basically all of these parts are realitively inexpensive, as long as you have the tools to swap them yourself.

I'd second the comment about cables btw, you can get a full replacement set of Jagwire cables for £20 off of Wiggle.  I found it a useful learning experience swapping them all (do get a decent cable cutter though), and it greatly improved the shifting quality after I replaced the 3 year old cables on that bike a few months back.

Good God! That red chain is going to make you go fast!

Re-reading your post, are you sure a good service/ re-index and clean and lube of the cables, along with a new chain won't solve your problems? Check the hang of your derailleur too.  Doesn't take much of a knock to put the cage out of alignment in my experience.

I'm loading my Pinnacle Arkose up with some panniers for a spot of camping/light off road and have found a 30 tooth cassette not quite easy enough for rocky moorland tracks. (  Shame on me!)

I've just fitted a Tiagra 34 tooth cassette along with Alivio T4000 (?) 9 speed trekking derailleur after spotting a comment on Wiggle's website. Seems to work OK with my 10 spd 105 shifters, if a bit noisy on the jockey wheels in the 11 speed cog.  Total cost under 40 quid. I'm pretty sure Chain Reaction or Wiggle have a Tiagra 10 spd 32 t cassette at a reasonable price. (As per Carton above). Good luck.

Don't get hung up about descriptions of "mountain" or "road" cassettes, there's no such thing really.  The Shimano SLX HG81 11-32 10 speed is £23 at Merlin, £21 at Chain Reaction.

SRAM PG1030?  Same 11-32 range as your old cassette, a bit dearer than the Tiagra at £28 from both Wiggle and Chain Reaction.  Same spacing and hub fitment as Shimano, so a straight swap.  

Both of these should shift a little better than the SunRace, but maybe that's just me being unfair to SunRace.

Personally, I would use a 10 speed chain with a 10 speed setup.  You can probably get away with using a 9 speed, but why would you?  Despite Shimano's protestations, any 10 speed chain will work - and you usually get a nice quick link with their competitors rather than a pin.

New chain and cassette will improve shifting experience. Keeping your chain in good order and lubricated will keep shifting smooth as possible. Unless you move upto 105, or Ultegra kit, gear changes will be a little less smooth. Kmc chains are excellent 10 or 11 speed. If you need 28 and 32t don't buy anything smaller.
It matters not if you use mtb parts on a road bike.
I made a setup on the wife's shopping bike which she loves but can't ride up Hills. It has 11-36 Cass, mtb derailleurs and shifters, works beautifully

Gear shifting isn't going to change significantly unless the cassette is really worn, at which point the chainrings might become an issue as well. You are going to get slightly better shifting from a Shimano cassette on a Shimano drivetrain. But going from a 32T to a 25T bailout gear is going to be brutal if you do any type of hills, particularly on a tourer. An MTB cassette will be just as well, however, your mid-cage derailleur isn't going to work past a 32T, and as MTB cassettes have gotten wider, it's hard to get an 11-32 10 speed Shimano one. So I'd say stick to your original thought and get an  11-32 Tiagra  one online: http://www.chainreactioncycles.com/shimano-tiagra-hg500-10-speed-road-ca...

Do shop around, but even if it was £40 extra I'd take the 32T over 25T for my riding, never mind £4. On the chain, you're better off with the 10 speed chain than the 11 speed. Cheaper and probably a bit more durable. Do swap the chain if you're getting a new cassette.