You need to look on Garmin's site at the product specifications. You can select a number of different models of the Nuvi and click to "compare" them. Look down the list of specs for "Routes" and make sure it's a number you can live with.
I did a quick check and most of the ones under $250 have 0 (zero) for "Routes". That means you can't load routes into them at all. So you need to select carefully.
Here's a place to start: https://buy.garmin.com/shop/shop.do?cID=134
You can play with the selectors at the left to get lists of models that fit those canned criteria or just leave it listing all of the models and go down the list on the right and click to select by your price range. Then click "Compare" at the top of the page so you can see which ones allow routes to be saved on the device.
By the way, the Nuvi 350 does not allow you to save routes to it. If/when you get one that does, you can look at the links Larry supplied. The first one gives you a complete step-by-step of how to do it, complete with pictures.