Headphones are not really optional for recording vocals, because you don't want the backing tracks to bleed into the vocal mic (usually).
Also, you should look at some kind of acoustic treatment. The best thing to have would be a walk-in closet where you can set up the vocal mic and headphones and put up some treatment to diffuse and absorb sound to reduce early reflections.
Regarding packages versus buying it in pieces - buying microphones, monitors, and headphones are all like buying musical instruments. No one instrument is the right one for every musician. You want to look at your budget and then get what makes the most sense to you. The problem with any package is that if you pick a package based on the headphones you like, then you're stuck with whatever microphone comes with it, or vice-versa. I don't see them really saving you much money either, especially if you get sick of one component quickly and want to replace it soon.
On that last point, it's better to buy quality equipment that will last and sounds good than to get something inexpensive that you'll want to replace, since the latter will cost you more in the long run.
The most affordable vocal microphone that you will almost certainly never want to get rid of is the Shure SM-58. It has a reputation as a live vocal mic but does get used on major albums, like Achtung Baby by U2. It would certainly work for House music. If your budget is bigger than that, look for classic microphones, not "affordable" microphones. Re-20, MD-421, SM-7, SM-57, AT-4033, C-451, are all good examples of classic mics at non-ridiculous prices.
If you can invest $80+ or so on headphones from AKG, Sennheiser, or Audio-Technica (depending on your preference), those should last and continue to please you for several years.
Audio interfaces still tend to become obselete after 2 - 5 years, so this is one area where I would look a little more towards saving money. Focusrite and PreSonus make some decent low cost interfaces.
Monitors are hard to buy, because under at least $1000 a pair they are full of design compromises and are just speakers sold by music retailers. Once you get up to the $1500 per pair and up market, it does become partly preference and partly a choice of which compromises you prefer. At the lower price points, I wouldn't worry too much about getting the best product, because they are all going to be difficult to trust.
