First off welcome.

How much space do you have and what do you have to haul your lumber home in? It will cost you in the range of 20% of buying a raised bed kit to build it yourself. For a 4'x8' 2x8 bed I would expect to spend less than $20.

I see you needing three basic tools
pencil
handsaw
hammer

If you don't have a saw you'll probably spend less having them cut the piece than you would buying the saw. Somewhere like home depot or lowes charges 25 to 50 cents a cut and will often times give you one or two free cuts.

I would suggest 2x8 untreated lumber for this. Treated lumber is about twice as expensive as untreated and can leach undesirable stuff into the soil (studies have pointed both ways). Treated lumber is darker than untreated and the tags will clearly indicate whether it is treated or not.

Untreated lumber will last 4 to 6 years before it is rotted out, usually.

Based on common lumber sizes 4'x4', 4'x8', and 3'x9' are the easiest sizes to build without scrap wood leftover. Eight foot and twelve foot lengths are the most common.

Filling the bed will be the most expensive part of this. Here are a few ideas to look into for this:
lasagna gardening - make layers of stuff and have it compost down in place
straw bale gardening - place straw bales in the garden and have compost on top of them where you have the plant planted, after the season the bales will be mostly rotten out and provide the composted base for your garden just turn this over a little with a shovel and your ready for next season
get a load of compost - this is the most expensive way to go but is instantaneous

I've done both lasagna and strawbales and have my own compost pile to supply my garden with compost. I live on a small property in the middle of a 158 thousand person midwest city while doing this.