Hi Lynda,
Welcome!
If you have a gym close to home, it would be great if you could try to join & get there a few times a week. But if you are set on working out at home, you DEFINITELY can gain strength & lean body mass at home.
If you could get a home gym, that would be great. If not, some free weights would be great: a barbell, 2 dumbells & free weights - plates & clips so you can adjust weight. You can just use anything to lay & sit on (coffe table, aerobics step if you have one). You might even be able to get used stuff cheap if you have a "Play it Again Sports" store or something in your area.
The other thing that would complete your home gym are dynabands!
www.spriproducts.com (xertubes) These are fully adjustable - you can easily & instantly increase the resistance by grabbing them lower, wrap them around your hand, etc. They are also very versatile (& travel easily!)
With some adjustable free weights & exertubes, you won't really be limited. You can follow any strength training program. Keep reading the board for great programs & be sure you are eating clean! try
www.fitday.com to keep & track, be sure you get enough protein & fat, etc.
1 hour of walking is great - but 3-4X per week max would suffice. Focus on that lifting & clean eating to get strong, firm, & lean!