The quickest way from Euston would be to take the Virgin service to Wilmslow (with trains departing every hour), then take a taxi to the airport – (a 5-mile journey typically costing around £12-£14). You could also take a train from Wilmslow to the airport – (a 7-minute, £3.20 journey with trains departing every hour and a relatively easy platform change). This route is typically quicker than going via Crewe (although there are more departures per hour to Crewe from Euston) and can be much easier re. platform changes. The only real advantage of going via Crewe is the amazing view you get of Jodrell Bank as the train passes by.

The nicest of the three hotels is the Radisson, although as has been mentioned, the others have a free shuttle to the terminals. (I normally walk from the Hilton, but wouldn't recommend unless you're travelling very light.)