It really depends on your play style I think.
Honest Hearts is both the shortest and least interesting DLC of the group. The only notable items from it are the .45 auto pistol (with its mods, I find it to be the best silenced handgun) and its unique counterpart A Light Shinning in Darkness (if you take the grunt perk it becomes the highest dps handgun and it even benefits from Pack Rat if you like playing in hardcore mode), the Survivalist's Rifle (an amazing gun that also benefits from grunt, although it fires 12.7mm ammo), Joshua Graham's armor (a very solid light type armor for crit builds that use the Light Touch perk), and finally the Desert Ranger combat armor (the 3rd best medium armor set in the game, losing only to the elite riot gear and the gannon family tesla armor. Although the Desert Ranger helmet is a 5 DT weightless helmet which makes it useful for hardcore).
Old World Blues is overall a very well written set of content, very funny and a bit creepy. It has a full set of craftable skill books, a fair mix of weapons including the K9000 (basically a minigun that uses .357 rounds), and its upgrade FIDO which uses .44 magnum rounds, the LAER (a high dps energy gun), Christine's COS silencer rifle (a unique silenced sniper rifle as an alternate to the GOBI if you like stealth kills), the saturnite fist (the super heated version is pretty good if you take the pyromaniac perk), and the protonic inversal axe (an anti-robot/power armor melee weapon with respectable dps even against non-robot/power armor enemies). In the armor department we have the valence-radii hats which provide +1END and gives minor health regen, the hazmat suit and cowl (the suit alone gives 85% rad resist, aka the max you can have, while the cowl gives you nightvision), and the amazing stealth suit mk II (which, when fully upgraded, gives +25 sneak, +1 PER, +1 AGI, +20% movement speed when crouched, and automatic use of stimpacks and med-x. you can get addicted to med-x this way and the stimpacks used this way do not make use of your medicine skill. Also, if you get poisoned by a cazador the suit will use a stimpack and heal the poison.) This DLC also comes with several additional implants that are not restricted by the normal implant limit. You also get 3 free perks just by going into Big MT, plus you get access to the GRX Implant perk which gives you free daily doses of non-addictive turbo. It also gives you access to several new traits at character creation. Skilled (+5 to all skills at the cost of -10% XP gain, you level fast enough that the penalty doesn't even matter) and Logan's Loophole (locks your level cap to 30 but you will never get addicted to anything) are the best of the bunch.
Lonesome Road adds one final set of skill books (yay min-maxing). It also has upgrades for ED-E turning the little eye-bot into, arguably, the most useful companion ever. It grants you craftable auto-use stim/super-stimpack and auto-poison cure recipies, a bitter drink recipie, and rushing water which gives a 50% attack speed boost (does not affect automatic fire weapons) for a few seconds and is non-addictive as far as I can tell. For weapons we get the blood-nap (a unique knife that can do even more damage and dps than chance's knife plus gives +10 sneak), the fist of rawr (a legit deathclaw gauntlet), 2 more unique grenade rifles, an actual rocket launcher (not missles, rockets), old glory a melee weapon with average dps, a nail gun (which can do respectable dps to low DT targets), the industrial hand (an auto-attacking power fist that ignores DT/DR and puts out high dps), and the amazingly silly, yet effective, shoulder mounted machine gun (it uses 10mm rounds to amazing effect. has high damage for an auto-fire weapon and puts out high dps to boot. It can only be repaired with copies of itself, even with jury rigging, so make sure you have repair kits for this baby). As for armor you can get a slew of nice medium and heavy armors, most notably the elite riot gear (with matching helmet it gives 28 DT, +5 crit chance, +10 guns, +5 speech, + 2 PER, +1 CHA, and sneak sight) and the scorched sierra power armor (24 DT power armor with +1 STR, 25 fire resist and HP regen of 2HP per second). For light armor you get your choice of 2 dusters, one from Ulysses and the Courier's duster which gives different bonuses and gets a different look based on who you side with for the final battle. A fair warning though, 3 of the perks from this DLC will be unattainable without all 4 DLCs as they require you to be level 50.
If you enjoy skill maxing then I'd recommend getting OWB and LR. With the addition of the skill books from the two plus the skilled trait as well as the comprehension and educated perks you can actually max all skills with an INT of 1. Of course with some simple math you can find plenty of ways to skill max with several other INT scores. Honest Hearts really is the worst of the DLCs. You get no skill books, the least interesting content, the least amount of content, and only a handful of worthwhile items.
Each DLC is tuned for characters of a certain level or higher. Dead Money is for 20+, Lonesome Road is best done at 25+, and Old World Blues can be done as early as 15+. Oddly, Honest Hearts can be done at nearly any level. I've managed to beat it by going in at level 8 (and doing every quest). The only thing I noticed is that the enemies had rather high HP for their level and my guns were not that great against them at first. It turned into cake once I got my first .45 auto pistol though. As for playing things in order, Dead Money and Old World Blues have some intertwined story bits and Lonesome Road is hinted at in OWB and DM. Honest Hearts is the odd duck out as it is not mentioned anywhere else in the Mojave or in any DLC, nor does it make mention of any other DLC. So if you are looking for story, then I once again have to say that you should avoid Honest Hearts at this point.
Hope that helps.
EDIT: Sorry, I forgot HH has one single line vaguely mentioning Ulysses. So noteworthy a connection I totally forgot about it. =\ (sarcasm if you didn't pick up on it)
