So annoying, and there's always the justification of "But the episodes are so cheesy and not as exciting as the new ones, [whoever I'm trying to get to like the show] might not get hooked!" Boo fucking hoo. If someone is so thick they can't enjoy any eps with Eccleston then I'm fine with them not being a fan of the show.
Bingo. There's some cheese in the first series, for sure, but it's hardly ever bad enough to ruin the experience. Even the Slitheen for me had redeeming qualities. Well, their episodes. Not so much the Slitheen themselves haha. Plus there's some important characterization going on in that first series, not to mention the fantastic quality episodes that are "The Empty Child/The Doctor Dances", "Dalek", "Father's Day" and "Bad Wolf/Parting of the Ways".
And as far as the cheese factor goes I can't help but cut the series some slack. It couldn't have been easy to bring back such a beloved show and I can imagine finding the right balance of old and new would be difficult. So a little cheesiness/silliness would be expected. Some of the classic serials are corny as hell and not just because of the dated special effects or whatever haha, but they're still enjoyable.