i know a service provider called aapkadomain.com.. their hosting service is very nice ... and you can contact them via phone or email. they provide 2 type of hosting 1st is where you need to manage the things.. 2nd is where they will manage the hosting for you.
I've been using hostmonster for 1 1/2 years and I've had next to no down time, quick contact, and great service.
I have read a lot negative reviews of them. Have no personal experience but bad feedbacks are more than positive ones.
I think marble host company is good host for Wordpress.
And they have active support with phone support.
What ever you do, do not use IXhosting.. they have incredible downtime.. it's super frustrating.
Any web host with cPanel and a auto installer like Softaclous or Fantastico should be able to meet these qualifications. The big hosts tend to stuff as many accounts as possible per server which leads to horrible speeds. That is something to keep in mind.
Wordpress can be a cpu hog if it gets big and alot of users. I have a vps at jaguarpc.com and moved over my daily blog.I run a blog about carrots and pumpkins this time of year and it gets alot of traffic.
It really doesn't matter which shared host you choose... the big ones are hostgator, and dreamhost. One thing you need to do is optimize your wordpress blog with a cache plugin such as w3 total cache. Decreases server load and increases page load times substantially.