Hello.
Thank you for inviting me to bid on your project. However, your budget most likely won't be enough to achieve the requested result. What is more, it is not possible to estimate the development effort without having access to the website and ideally to the code itself.
With regard to what you want to achieve, the page load time depends on many factors - server performance, the number and size of images loaded, the size of the web page, the number of plugins used and so on and so forth. If your server is slow or overloaded(not unusual with shared hosting), no matter what we do the final result won't be great. If the home page(for instance) contains 20 images with size 3 MB each and if you want to keep the number of images and their size (because decreasing the size would affect their quality), then again there is nothing to do.
However, I have been achieving rather good results in optimising Wordpress websites. What I would try is to combine the css and javascript files on order to reduce the number of requests to the server, to check for slow mysql queries, to minify the code, to set up a CDN and suitable caching mechanism. If you were using a VPS then I would install a dedicated software for caching a minifying which gives much better results that the popular Wordpress plugins.
Best regards,
Kremena