Brilliant strategy, btw, iwantitiwinit.
For the OP, since your budget is limited, I would recommend purchasing the most valuable cards and the HOFers initially. That way, if you decide the set is becoming too expensive for you, you can sell off what you have easily or switch to a HOFer only set instead of having a bunch of commons on your hands. Once you decide the set if for you, and that you should have the means to complete it, I would look into buying lots. You will save money over time buying lots since you can re-sell (or trade) the duplicates that you have. You can cherry pick the lot for the cards that you want, so if you want to build a mid range set, you can pick out the better cards or if you just want a lower grade set, you can get rid of the higher grade ones. After you get a substantial part of the set done, you would look to buy individual cards. Buying cards one by one will typically be more expensive. However, you can set snipes on ebay to slowly buy the cards that you want at the prices you want in the condition you want. Do your research so that you don't overspend for cards in a particular condition, and have fun! Good luck!