With so many options to choose from, it's easy to get lost in all the details so hopefully this will break down the most important ones.

Made from one solid piece of wood. It comes in widths between 4 and 8 inches. It can come pre-finished or unfinished.
Because its natural wood, usually it needs to be glued and nailed to a sub-floor. A sub-floor is a rough surface underneath your finished floor. usually made of concrete or plywood. Because this involves glueing and nailing, you're probably going to need to hire a professional. Lastly, make sure you leave the wood in the intended room for a few days to let it acclimate to the temperature. Natural wood tends to shrink and expand depending on the temperature and humidity.
There are many pros about natural wood such as how long lasting it is. Being made of thick planks, it can be sanded and re-finished over years. Hardwood is also very versatile with all the different species and colors but there are some types that are used more commonly than others. Oak is probably the most common and it is known for being warm and having character with many different variations like red, white, domestic and imported oak. Maple is also pretty popular as well but is much lighter and a bit more difficult to stain. Walnut is rich and dark and know for its almost luxury look. Hickory is a hard wood that's varied and rich with complex detail. Bamboo, while a unique option, is eco-friendly and very durable. Lastly cork, which is really a composite made of bark and pressed into plank is another option.
The main con about hardwood is that it's susceptible to temperature, humidity and moisture. it can also be warped, scuffed and dented easily depending on the material. It may require some maintenance and it tends to be pretty costly.
You can place hardwood in most places in your home but make sure to avoid anywhere where there will be water or any drastic changes in temperature.

Engineered Hardwood:
Made from 2 or multiple layers, with a thin hardwood top layer and plywood or fiberboard layers below. Can come in sizes up to 12 inches wide.
It can be nailed or glued to the sub-floor, or as a floating floor with click together flooring. Clicking together can be done by oneself but will take a bit of time and skill.
The pros are that it's very similar to the look and feel of hardwood but much more resistant and comes in multiple sizes. It's also more environmentally friendly than hardwood and a bit cheaper than hardwood.
The cons are that it won't last as long as hardwood, nor as many options as hardwood.
You can really put it anywhere as long as it doesn't get wet.

Made from the base layer of fiberboard with an image layer and a transparent plasticate layer that protects from wear and tear. The fiber board is rigid and high density, similar to the core or of engineered wood. The photo realistic image layer mimics wood, stone, tile all the way down to the grain detail.
Laminate is usually installed as a floating floor installation meaning that the planks attach to each other and not the floor. This usually requires a soft underlayment like foam underneath.
The pros are that it's very durable especially when it comes to scratches. It's easy to clean and UV resistant. It's also a lot less expensive than other types of wood.
The cons are that it's not waterproof and will swell if water gets onto it. Can be very artificial looking. It also feels like plastic and slippery when wet.
Because it's scratch resistant, this will work anywhere where theirs high traffic except for places that come in contact with water.

Vinyl Plank:
It's a synthetic flooring material that mimics any material. SPC stands for stone plastic composite vinyl. It's made from layers, vinyl base layer, vinyl design layer and protective layer. The base layer made of vinyl can range from rigid to flexible. The design layer is also made of vinyl and mimics and texture. Some products have backing underneath the base layer for rigidity but it depends on the product. You can also find rigid core and flexible core products as well that add comfort and durability to the bottom.
There are many different ways you can install vinyl. You can glue it down, click-lock it, floating floor or loose lay which is an installation that relies on friction and weight.
The pros are that it's comfortable and durable. It's 100% waterproof and inexpensive. Also has a low installation cost.
The cons are that it's plastic and not environmentally friendly. It can also look sometimes artificial.
Since its waterproof, you can basically put this anywhere, even outside.

Many different types of material such as stone, ceramic, porcelain and cement. Stone tiles can include marble, granite, sandstone and many others. Ceramic tile is made of baked clay and is loved for it's natural feel. Porcelain is made of a finer clay and baked at a higher temperature, making it less water absorbent and less crack prone. Cement tiles are quite popular in Europe for their particular style. They cure at room temperature making them porous but they can be sealed and refinished. You can also have them glazed or unglazed. Unglazed is a bit more rough but it keeps its color. They are usually more rustic and slip resistant. Glazed, as beautiful as it looks, means that cracks become more apparent. That said, they don't stain or absorb water as much.
The installation is done by laying the tiles on grout. The subfloor and mortar has to be prepared before one can go grout tiling. A backer board can be laid down then the tile.
The pros are that tiles have a timeless look. They are also waterproof and easy to clean.
The cons are that they are brittle, can crack or chip. Even some stones can stain.
These can really be put anywhere but just be careful about chipping or slipping when it come to glazed tile.

Hopefully this breaks down all the necessary details about which flooring option to chose.