Janet, safaris can be expensive, but for the price of 2 people on a safari tour, you can afford a modest accommodation bespoke tour. That is why I suggest the Tanzania TripAdvisor forum. I am a solo traveler and certainly not wealthy and can manage it. I did find an agent to work with me within my budget but they are under new management now and not sure whether it would be feasible any longer.
There is website that makes it easier for us, as you feed in your wishes, budget, etc, and the matrix comes up with options for you. You can at least look at this website for price comparisons. https://www.safaribookings.com/ to see if it could suit you. As it is a bit of a one size fits all sort of thing, I would still prefer to work with the offering company directly, but you can at least see what is on offer.
A car and driver will be less, as he is not necessarily a licensed guide and won't have the same company overhead.
Fodors puts out a Safari Planner. Unfortunately, it hasn't been updated in the past few years, but if you can get it from the library, it is worth a read to perhaps narrow down your country choices. Realize, however, there has been big changes in some countries as far as safari costs and offerings and niche markets.
There is no doubt a tour or bespoke travel would be a lot easier for a neophyte, but if you have visited 3rd world countries previously, then you may have less of a culture shock.
I mentioned South Africa because it is the most 'civilized' with lower fees and tarmac through the parks. Many drive Kruger on their own. Namibia is totally different than other countries, but can be driven. The arm at the top is greener than the bulk of the country. Botswana markets to the rich and elite. I read this book and chose Tanzania for the biggest bang of animals. The Serengeti, Ngorongo Crater and the masses of animals that congregate and migrate were the draw. I fell in love with the Serengeti and the country drew me back several times before I had to close that door. There is also mountain birding east of Arusha and Moshi heading towards the coast that isn't often explored. There, lodging can be rudimentary, but very affordable. Kenya spends a lot on advertising, but doesn't have the longest season for herds compared to Tanzania. There are options to head out to camps and pay per safari drive. You are sharing a vehicle with up to 8 others, or be offered a van drive (with some sort of pop up roof). This is how you can reduce the budget, but whether any camp will satisfy your birding activities, I am not sure.