Speed is what your site needs. Especially, if you have a good day and a lot of visitors. A good host will bring you a fast start, but unoptimized images can make pages load very very slowly. Your visitors patience is limited.
BUT there is an exaggeration to this. You need an optimum between resources you spend and gains.
In my opinion, starting with free solution is perfectly fine. Please note that the most image optimization plugins are not free, they work on a freemium model. Basically, they allow you to optimize a few images and they ask you for money after that. Why? Because they offer convenience, and because they process your images on their servers. One argument in favor of clould image optimization is that it takes some power to do it, and regular small hosting plans don’t work well for this.
However, you can do it
- By using plugins that automatically resize the images upon upload. They are not necessarily image optimization plugins, because they don’t take large images and re-write them accoridngly with some heavy algorithgms, that reduce the infromation from an image, while keeping the same aspect (at least for human eye). This resizers are more brutal than the image optimization services, but they are in most cases good enough.
- Locally optimized images. Photoshop or any other image editor. There is a downside to this approach. When you upload an image WordPress generates a number of images, called thumbnails, that will not be optimized.
- Third solution is to use free plugins. They are not perfect, and sometimes their features are limited. For example, you might find that you don’t have a backup for your pictures. Best way is to backup your site, optimize your pictures, see if they can be reverted to the original.
- Forth solution is the most simple. Purchase an optimization plan.
- Keep an eye on deal sites, sometimes these providers come with lifetime deals.