The vampire attacks don't occur unless you are there, so if you are not going to do Dawnguard right away, then go to Solstheim right away.
You can go there as soon as you can get to Windhelm, go to the docks and talk to the boat's captain: Gulmar Salt-Sage.
You can do most of the quests in Solstheim before you even become dragonborn, but you have to complete the main quest up to visiting the Greybeards, in order for Miraak's cultists to attack you and start the main Dragonborn quest-line. Then just go back to Solstheim right away. I did that and had no vampire attacks at all.
I didnt ever get Hearthfire becasue i didnt find it worth the money, the other two are good and its up to you what order to get them (i got dawngurad before dragonborn) --- GT-Elduka1 (if you want to add me tell me your from here)
Hearthfire's just for housing, essentially, though it can be useful for alchemists (you can grow your own garden and the like). Can be fun for roleplaying.
Dawnguard adds quite a few enemies to base Skyrim, improving the game in general. It primarily adds, however, a main questline and two different factions to support through said main questline. Dawnguard adds lots of weapons, alchemy ingredients, armor, and some magic, as well. Big selling points for Dawnguard include Crossbows, improved vampires, the powerful Vampire Lord ability, a shout that summons an undead dragon, as well an artifact that has the ability to "shut off" the sun for 12 hours, or turn it back on by reading one of the Elder Scrolls you find during the questline. Useful for vampires. Dawnguard adds three shouts to the game.
Dragonborn adds the isle of Solstheim for you to explore - Solstheim could previously be visited in the Bloodmoon expansion for TES III: Morrowind. As such, it likely will set off quite a few nostalgia bells, but that's not the main point: there's plenty of new quests, items, dungeons, and goods for you to find. Dragonborn, in my opinion, is the best expansion, as it not only ensures that you have an abundance of unique quests, but many of the powers and items you find in the expansion have completely unique abilities rather than just strong enhancements. Both finding and using items from Dragonborn is a lot of fun. Big selling points for Dragonborn include really cool and unique shouts, really cool and unique abilities, really cool and unique artifacts, the ability to explore Hermaes Mora's realm, and the ability to ride dragons(which isn't as good as it sounds, but still!). Dragonborn adds four shouts to the game.
Finally, I should note: Dawnguard DOES add vampire "attacks" to the game once you hit level 10, and the attacks have a chance of occurring every time you enter a city at night, at least until you finish Dawnguard's main questline. However, many people make these attacks out to be much more problematic than they actually are: #1. The vampire attackers will only begin attacking people when you get close to said attackers. Until then, they try to remain as anonymous "travelers." #2. Vampires NEVER ATTACK if you are not in the city. #3. Vampires can only attack if YOU ARE IN THE SAME CELL(map, so to speak) that they are. If you go inside a building or leave the city, they won't keep attacking, if they even started attacking in the first place. #4. If you save often(or have proper autosaves on) you can just reload should an attack break out AND it kill someone you like. You and the city's people are usually capable enough to prevent any deaths, and you can reload if someone you like dies. #5. If all that still bothers you, travel to nearby the city, then wait for daytime before entering it. I doubt that'll be necessary, however. This method likely won't work for smaller settlements like Riverwood, though I'm not sure what settlements the vampires can attack. (They have attacked a smaller settlement I was in before - I think it was Ivarstead that they attacked, at least for me. I'm likely wrong.)
In short, vampire attacks ARE NOT AS BAD as many people will make them seem. It's almost a running gag on this board to exaggerate their lethality. Just pay attention to music changes, your compass, and guards drawing weapons - and if all that fails, just be sure to investigate the city after you wander around it at night, though it's likely not necessary. There will generally be a sign that there is/was an attack. Completing the main quest of Dawnguard FOR EITHER FACTION will stop the attacks, as well. --- Some people seek argument - sometimes it's best to deny them that by ignoring certain topics. In general, be kind.