Venice, Italy to Arosa, Switzerland

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Hi!

I am trying to figure out the most enjoyable/cheapest way to get from Venice to Arosa - what do you suggest?

TIA

"most enjoyable" in sense of sightseeing will be route via Tirano-Poschiavo-Pontresina (so called Bernina route), but it would be difficult to save on the leg Tirano-Arosa, since discounted tickets on the route is not available (you can buy them only on part St.Moritz-Chur-Arosa), thus you will need to pay full fare, which is 59 CHF (Tirano-Chur) or 68 CHF (Tirano-Arosa).
The only way to save (around 10 CHF) there is to purchase full fare Tirano-St.Moritz, then SuperSaver discounted tickets for part St.Moritz-Chur and Chur-Arosa (need to buy those in advance online). Venice-Tirano via Milan using regional trains cost app. 20 euro, if to use faster EuroCity trains for Venice-Milano leg, then you'll pay from 10 euro to 20 euro more.
You can also travel via Milano-Como S.-Lugano-Bellinzon-Chur, but it will take app. the same timing and you will need to do more 'tricks' with tickets in order to spend around same sum as via Tirano. Full fare via Como-Lugano will be more expensive, then via Tirano.

Thanks so much for responding! Can you explain step by step where I would need to get on/off and where to buy the tickets? I am trying to plan a vacation and really have no idea where to start.  The only way I was able to find to go was with the Eurorail and it was very expensive. like $389 per person!

'Easy' daytime option (example for 20/01): 8:58am EuroCity train departure from Venice-St.Lucia, arrival to Milano Centrale at 11:25am, then you wait for regional train from Milano Centrale (12:20) to Tirano (14:50). Full fare for one through ticket Venice-Milan-Tirano cost 39.25 EUR (if you purchase ticket in advance, then you get -30% discount). In Tirano you will have 50 minutes to purchase ticket till Chur/Arosa (fares quoted in above post), then you will need to make couple changes:
 
All of the trains on the route from Tirano till Arosa wait for each other in case some a late.
'Cheaper' option: combination of regional trains from Venice to Milan and then to Tirano (use of regional train all the way from Venice will save you up to 15 EUR per person), dep. from Venice at 7:41am, 2 hour layover in Verona, arrival to Milan at 14:00, to Tirano at 16:50, again 50 minutes till next train to Switzerland. As result, you will arrive to Arosa 23:58.

Wow!! This couldn't be better - thank you so much for your help!

Just in case:
Swiss trains timetable and fares - http://fahrplan.sbb.ch/bin/query.exe/en?
Italian trains timetable and fares - http://www.trenitalia.com/cms/v/index.jsp?vgnextoid=c79686605528a110VgnVCM1000003f16f90aRCRD
Best website for all European timetable - http://reiseauskunft.bahn.de/bin/query.exe/en?newrequest=yes&protocol=http:& (website of German railways)