did you look at the picture below this thread ? It is fairly basic by it's design. If you went with out door treated wood ,you wouldn't have to complete it all at the same time. That means you can do it phases and you don't have to use the same builder /contractor for each phase, unless of course the contractor is working with you in your budget. I built one that way for some people, after it was framed in, they painted it. 4 months later I roofed it. Two years later I with their help I closed it in ,changing it to a screen windowed patio I suppose you would call it that. That phase in was done over a weekend.
They saw it as an extra room ! Some lights and plugs and they added a tv and a small chill box !
The power was already there ,one outdoor plug and back door or patio lights. Just changed the arrangement around somewhat.
The benefit of being inside and outside bug free ! Kind of like an additional room add on more on an outdoorsy scale.
Since than a a deck was added in front of the closed in patio ,later railings were added to the deck complete with pickets and two gates. Their kids got old enough than they added a pool. That was over 20 years ago.Same house ,same people and a lot of work was done over the years.
They saved money ,I made money, that's how it works. As time went on the projects got more involved and the budget moved up too.
My point is where there is a will there is a way- stick with it.
You can find an independent contractor in home repair that will work with you in your budget.
And you can have the materials delivered,so all the contractor has to do is get there and build it. The contractor will most likely hand select the materials than have them do the delivery.
Home depot or lowe's is a good a place as any to get the materials for an out door project such as what you have in mind. The contractor will give you a list of materials needed and cost.
That way the contractor isn't doing it on time and materials, just straight time. Easy bid ,easy job.
You can do it.!