Least expensive and most effective are not always compatible goals.
If using free wifi whenever you can find it is sufficient for your needs, then you need go no further than suggested above.
But, when you say “on the road” and that includes needing it literally while driving on the road so you can use GPS guided navigation through something like the WAZE app or a phones native GPS integrated into it’s system like with an iPhone, then you need to start looking at cell companies which offer unlimited data (Internet) plans.
Many of them are pre-pay and don’t lock you into a monthly contract. Therefore if you aren’t going to be continuously on the road needing Internet every single month, that may be financially attractive.
Off the top of my head, there are a few companies offering unlimited data plans. One is Straight talk available through Walmart. Another is MetroPCS which has stores all over.
So, how much Internet will cost you on the road is dependent mostly upon how often you find yourself needing it and whether or not you need it for navigation while driving
I only mentioned two companies that I’m sure have an unlimited pre-pay option for Internet. I’m pretty sure that if you do a little research , you’ll find others as well.