I would recommend a touring bike. They have what is known as a "relaxed" geometry which makes the bike more comfortable and more stable.
I ride a Surly Long Haul Trucker, which is around $1000, but I paid a lot more for mine because I had it customized with a lot of higher end components. Likewise you'll probably have to spend a bit more to get Tiagra stuff on there instead of the default configuration.
But I must stress how comfortable I've found tourers to be.