A smartphone is a phone that does more than phonecalls. The Samsung Galaxy range are good because they have very good sensors ( GPS, heart rate, gesture, gyro, geomagnetic, accelerometer) and reasonable battery life when using GPS. The S5 is waterproof. I think the Sony Experia is too, or you can get special outdoor military grade ones. With a 3g or 4g sim, you have full intenet access while you're cycling so that you can use satellite images for navigation on the road, or you can download all the satellite images and maps using wi-fi before you set off. Everything for cycling navigation is free. It doesn't cost a penny once you have the phone. You don't even need a SIM.
There's lots of other good smatphones too. Use Google to find the 10 best ones or whatever. You can buy Chinese ones for about £80 that do everything you need for cyling navigation. I just bought one of these to try because I want to temporarily use two SIMs at the same time:
http://pages.ebay.com/link/?nav=item.view&id=231615526395&alt=web