Aside from a momentary drop in score, a single HP is meaningless.
I don't view the HP a waste, but rather an indication that at this moment, your credit is insufficient for new unsecured revolving TLs. In general, after a declination, you should (1) request a free hard copy of your report, and (2) review and address the reasons for the decline. In general, waiting for 6 months before another app after a declination is both prudent and standard practice.
From my experience and reading of others, I suggest the following during the building phase:
1. Refrain from app'ing for 6 months.
2. Use your Discover for all of your bills. Of course, pay your obligations by the due date.
3. In 6 months, if you can, open up 3 TLs - ideally, with an HP in each CRA.
4. This is important. Each TL ideally should be a "Prime" Lender (Chase, BofA, Amex, Citi, US Bank, Cap One, Wells, etc...) and NO ANNUAL FEE.
5. If possible, reach 5 no annual fee TLs asap each with a different lender.
Many will disagree and find my recommendation too ambitious, but it will yield better results. If I were building/rebuilding today, it is exactly what I would do.
Several years ago, based on Fico's algorithms (assuming they haven't drastically changed), I informally calculated the score's ascent comparing a few TLs vs. a larger amount. All things equal, a greater number of initial TLs (5, beyond that you're hitting diminishing returns) leads ultimately to a higher score and thicker file in less time. Not sure if we can find it, but, if memory serves, Revelate had a post illustrating this very dynamic.
In the end, far and away the most important is to use your cards and meet your obligations.
Good luck!
*Edited* PS - By the way, if you can be added as an AU on a 20 or 30 year TL with perfect payment history (like your Parents or family friend), in 6 months, you'll probably be auto approved for 2 or 3 accounts immediately with the above mentioned lenders.
