In order to rebuild, you have to draft well, period. That part is a given. No amount of FA's can be signed that can overcome poor drafting over a period of time.
However, FA is still a key way to acquire talent for your team. Ideally, we would have drafted well, and would have spent part of our existing salary cap space on re-signing players that we wanted to keep. Unfortunately, we don't have too many of those.
FA is also a good way to fill obvious holes BEFORE the draft, so you can concentrate on BPA, without getting forced into drafting for need.
We have money to spend, and we will spend it (a good part of it anyway). The team would by lambasted be everyone as cheapskates if we stayed 30+ million under the cap. The real key is managing FA, not making stupid pick-ups, not creating a salary cap hell in a couple years because we didn't do our homework.
1) don't over-pay for players on the down-side of their career
2) if you must sign an "older" player, keep it to a 1, 2yr deal. less risk to salary cap if you have to cut them (one of the biggest issues in cap management is having $$ tied up in players that are not on the roster)
3) make sure you retain flexibility for future years (make sure contracts on the team are such that next year, you will have some $$ to spent)
4) make sure you sign players who will work in your scheme
5) if you sign someone to a big, long-term deal (4-5yrs), make sure it's reasonable that the player will still be in their prime for the whole contract (signing a 27yr old player to a 4 year deal is probably ok, signing a 33yr old player to a 4 yr deal probably is not)