I quote from an online article concerning saws of all kinds.
A jigsaw is a handheld powered saw. It has a smaller blade and finer
teeth than a reciprocating saw. It moves vertically. You can change
the speed to make it go faster or slower. This saw is designed to cut
curves and other non-straight lines.
This is a useful article to skim through from end to end. It is quite comprehensive.
Each type of saw is described briefly. If you think a particular saw is best for your purposes then it is a good idea to search online for a saw of that name.Very often YouTube will have a video showing how to use it. For example http://bitly.ws/96y6
In the case of a jigsaw you need to distinguish when searching between "jigsaw puzzle" and "jigsaw cutting".
Note that jigsaws are mainly used for cutting (curves) in sheet materials such as plywood. If you want a clean cross-cut (as hoped for in your photo) then try searching online for "cross-cut saw".
You don't have to buy every kind of saw going but it helps to read a little (and perhaps try searching for example for "general purpose saw" etc.).
To avoid a lot of initial expense, it is worth considering buying hand-saws. When they are new and their blades are sharp it is surprising how quickly they can cut. Take note of other answers. When using a drill or a saw, always let the tool do the work, it is rare that a lot of pressure is needed.
If you find yourself working hard, then you may have the wrong sort of blade but, more likely, the saw has become blunt with use.
Arnold Schwarzenegger could probably saw with a blunt blade and I've seen builders with big muscles labouring away with a rusty and blunt saw at a rough plank. They get there eventually.
Hand saws can be reset and sharpened but it's a skilled job. Quite frankly, these days its cheaper to buy a new saw than go to the trouble. For power saws, check the blade for signs of wear after use and consider replacing them if they are bent or damaged. It saves time and money in the end.