Great chair. I can't imagine a slipcover unless custom made, fitting that chair without losing the very nice features of the chair. I haven't priced slipcovers for many years and the price will vary widely by location so first check to see what that cost would be. If it's out of your budget, then here's another option.

The actual upholstery fabric looks to be in good shape but a little dirty on the arms. I'd check into having it professionally cleaned by a very good service. Call a company who does fire/smoke restoration and try to get a recommendation. Professional cleaning might cost $250 but you'll be amazed at the results. A friend had a squirrel enter her home through the chimney while she was out of town. The squirrel walked all over her new white linen chairs leaving sooty footprints everywhere. A professional cleaner made them disappear. It was unbelievable. Took two treatments but it worked. Don't try cleaning it yourself. Without the correct products and skill you'll just sink the dirt into the fabric more.

The other option is to reupholster it yourself. The fabric alone can cost close to your budget but you'll have learned a good skill for now and the future. I learned by using a how to upholster book. Now that you can see everything on youtube, it is even more learnable.

But my first choice would be to get it cleaned professionally and save up for a pro to reupholster.

I would need to see your space to really know why this does not work. I think this could be done DIY and as mentioned you would gain a new skill. I do think that is not for everyone. I agree have it cleaned and for now a throw in a color that works in your space . There is no way to get a one size fits all slipcover for that piece and by the time you buy a custom one it will be expensive so IMO wait to have it done right.