What are the benefits of a high TTL for DNS?
Solution 1:
You're right, the main disadvantage of using a low TTL is that you'll end up dealing with a higher query load than with higher TTL. That said, as long as your DNS host doesn't have any problems with handling the additional load, then go ahead. Honestly, if they had concerns about their ability to handle the load, they wouldn't let you set a very low TTL for your records (though many do tend to recommend that you set your TTL only as low as is necessary, which is a sound recommendation due to the user-experience point that ceejayoz made).
Additionally, I should mention that many ISPs DNS resolvers completely ignore the TTL setting and just set their own cache expiry on records, so for many cases, changing the TTL won't actually make any difference in the amount of queries that end up hitting the authoritative servers for your domain.
Solution 2:
High TTL means ISP and client-side DNS caches will last longer, which means your site will be more responsive for return visitors or folks who spend a lengthy time browsing your site in a single session.
Some providers also charge you on a usage basis for DNS lookups.