We have recently bought and moved a 40-year old farm house to our ranch in eastern New Mexico. It has hardwood subfloor in 1/2 of the house (the oldest part) but it also has vinyl flooring I-mean-glued-on! It is level and solid. The other half of the house is large planks subfloor with thick plywood on top. Originally we had intended to use the old hardwood subfloor as our woodfloor in that part of the house, but seeing as the vinyl would be very difficult to take out, we are now considering getting either woodplanks (I like knotty pine, common grade...) or possibly engineered (not laminate, don't like the feel or look of it). We are trying to keep our costs down, and are doing the whole remodelling ourselves. We do not have a lot of time either. We want wood flooring throughout the house except bathrooms, but including a large country kitchen.

If we want to put floor on top of the existing vinyl, should we consider engineered, or go with solid t/g planks? And if solid planks, are there any disadvantages getting very wide planks, such as 7"? Any advice or suggestions would be very much appreciated.

New Mexico is on the dry side. I'd stick with strip oak, not wide planks. Nail down is best, in my opinion. Nail it through the vinyl.
Solid is a good way to go and can be less costly if using a lower grade. Lower grade does not mean lower quality. Lower grade means more knots and imperfections in appearance. In fact, the clearer (higher grade) the wood, the softer the wood,,,,,, generally speaking.
Cost effective is nail down, common (or less), strip width (less than 3.5" width) and sand/finish on site. More work, but less costly.