Firstly, just to confirm, you're clearly talking about the new series that started in 2005 - correct?
Okay, yes, the first four series are only available on DVD - they were all shot in SD, so a Blu-Ray release is unlikely.
After the fourth series, they had a year of special episodes - The Next Doctor, Planet of the Dead, The Waters of Mars, and The End of Time (a two-parter). These are collected in a box, "The Complete Specials". These are available on Blu-Ray - they started HD for Planet of the Dead, but the Blu-Ray box also has an upconverted version of The Next Doctor.
Then there's the fifth and sixth series which are both available.
We're currently in the seventh series - the first half aired late last year (and is available as Series 7 Part 1), then there was a single Christmas special, and the rest of the series starts again next week. (There will no doubt be a complete series 7 Blu-Ray release later in the year.)
And in terms of price drops, I see series 5 is currently $35 at Amazon. And I would personally recommend series 5 as a starting point. It introduced the current Doctor, a new companion, and the show had a new showrunner at the same time. So it was consciously intended to be a clean slate and an easy starting point for new viewers (although I would strongly recommend you try to watch the Silence in the Library/Forest of the Dead two-parter from series 4, just for the introduction of one key character).
(I also personally think the current showrunner is better than the previous showrunner, who I would often have issues with).
There are lots of single releases - they picked up a pattern of releasing DVDs throughout the year, and then releasing a combined box at the end. But I believe the sound is better on the combined box (I certainly know the earlier single disc releases only had 2.0 sound and you needed the complete series boxes for 5.1), and I believe they usually don't have special features.
Christmas specials are included in the complete series boxes - so as long as you've got the six series plus one specials boxes, you'll have everything you need to have.
(And obviously there's also the classic Who releases - most of those are individual releases with one multiple-part story per disc, although a few of those have been released in boxes - sometimes logically grouped, sometimes not. I'm pretty sure you're not talking about those, but I just felt I should acknowledge their existence. There's a lot of great stuff in the classic series that is worth digging into.)