What is the proposed material, diameter, and wall thickness? This has a great bearing on choice of tools. Looking at the HF tubing bender, it doesn't appear that it will do the job. Grizzly has a manual tubing bender for around $400 that is capable but you will also need a die. The die will cost another $120 to $160.
The important thing about bending tubing is providing side wall support to avoid collapse. The thinner the wall, the more prone to collapse. To that end, having a proper die is essential to making nice uniform bends.
I have a reputation of having OCD regarding restoring old vs discarding and buying new but I would consider this task carefully. By the time you have purchased the materials and the necessary equipment, you will have a considerable investment. Many of us are guilty of spending $100 on tools to save $10 but is is usually with anticipated further use of the tool. This, of course goes out the window, if the wife is insistent on restoring the furniture for sentimental reasons or if it is necessary to provide an example of why it is good for you to be buying all those tools.