You are correct the direct line to Warwick will be from London Marylbone station.
On the current winter timetable there is one direct express train every hour to Warwick with only 3 intermediate stops and it takes 80 mins.
Note that Lemington Spa station is also on that line and is the stop before Warwick is also close to the hotel with the added benefit of a train every 30 mins rather than every hour to Warwick so when looking for hotels you might want to look at both of those areas if you can't get into a hotel anywhere closer.
Expect a cab fare of about £12-£20 from either station to the con hotel on my ready reckoner.
As for tickets there are cheap "Apex" fares for £12 each way per person, these are limited tickets which means you can only travel on your selected train and are only avaliable 12 weeks before travel and on some lines these go very quickly.
More open tickets are avliable and travelling off peak (between 10am and 3pm and after 7pm at night) you can get an open ticket which is about £29 off peak.
Note the summer timetable may be different and fares will be going up anywhere between 3% and 15% this January.
If you go to this website.
http://www.chilternrailways.co.uk/You can search timetables and see fare options and even set an email reminder to be told when the cheap tickets become avaliable.
I don't know about being sent tickets overseas but you could buy them and have the option to collect them from an automated ticket machine using the card you paid for it. You need to check with the railway operator though.
If you want to know anything else just shout.