Absolutely! But you are in the ballpark. I would like to point out the matter of priorities - you obviously need a good sleeping bag and a comfortable pack of proper capacity, and those are items that probably will require a substantial outlay. Stove and cook kit are a different matter. A lot of folks get on fine with home made alcohol stoves and beer can pots - expenditure is negligible. You can do fine with an inexpensive tarp, provided you avoid extreme weather. I had almost ten years of extensive outdoor, overnight experience before I purchased my first tent. Many really good pads are pricey, but a cheap blue foam pad still does fine for me. YMMV. There are acceptable alternatives to a water filter that require much less initial outlay.

Make sure that your first trips are short, in good weather, and you can work your way down to the deep end of the pool as you gather experience.

Eventually you will spend far more than $750....