Frame making is very creative and yet, very exacting. There are no rules about what you can use to make them. That's what makes them so much fun to make. It's about making something that enhances the appearance of the art work, but doesn't overwhelm it.
I make picture frames from pine, but it is very carefully selected. I found some7/8ths by 4 inch pine at HD that often has long stretches that are knot free and grain without twists or other warps. Sometimes I just use part of this material for frames. It is thick enough for both a nice front profile and a half inch rabbet for the canvas. But when I can afford it, I love working with Cherry. It takes a deep, rich choclatey finish. It is easy to work and route. You might also want to look at the Yonika bit sets for picture frame profiles. I have also used chair stop you put on walls. This gives you thickness to work with. I have also used 3/8ths decorative trim and instead of cutting a rabbit, just gluing on strips of pine to create thickness and space for the canvas.
My wife is a painter and I get serious husband points for making frames for her. She bought me a special tool, a Lyon miter trimmer (Grizzly brand). You cut slightly long miters then use this double sided horizonal guillotine to shave it to an absolutely perfect 45 degrees. It has been around since the 1880 for making frames. You shave off 1/32nd inch at a time.
Gluing the ends of your frames makes for a weak joint. So I generally add a spline to all four corners of each frame. You can also glue on overlapping wood pieces to the back to form the rabbet and reinforce the joints. I prefer the spline as shown here.
To hold corners together and keep the frame absolutely square, I use simple spring clamps, like these. They only work if your 45 degree miters are dead on and the sides and also the top/bottom are cut to exactly matching lengths. If they're not identical, it's impossible to square up the frame.
You have to measure the painting or art very carefully and cut lengths based on fitting the painting into the resulting rabbet. I physically fit the frame to an oversized piece and then cut to the that point. I want the lip of the frame to overlap about half an inch over the edge of the painting. So I leave the rabbet about an eighth inch longer than measured.
To hold the painting in place, I got what looks like a stapler, but it shoots a small metal tab into the frame to hold the art in place. It looks like this.
Here's what the Grizzly miter trimmer looks like. It is incredibly sharp and I have it mounted on a piece of ply with handles so I can keep my fingers from being sliced. Ask me how I know that.
Sanding all those inside and outside curves is almost always necessary. On pine, I always use sanding sealer. And I discovered 3M's flexible sanding medium, which is so much better than sandpaper that I stopped using anything else. I only sand to 220 grit, any more is counter productive. And I use shaped sanding blocks, which I got at Rockler for cheap. With the 3M stuff wrapped around the blocks, sanding goes really fast. I start with 120 grit, then 220. Some go higher, but I think it only raises fuzz.
For a perfect glossy finish, forget sanding and use a scraper, there are many curved scraper shapes that work. This is a pretty standard mix of scrapers with a burnisher to "sharpen" them. Violin makers use these to make perfect foundations for their stain and varnish.
I use a sliding miter saw to rough cut corners, then the trimmer. But you can do this on a table saw. I use my reliable Freud industrial Glue Line for stuff like this, it makes a baby behind smooth cut. I also recommend you pop for an incra precision angle gauge. It is very precise and the long support arm allows you to use a stop block for exact same length cuts. Unless you buy the miter trimmer, this is my recommendation. It's a peach!
Cheapo miter gauges are rarely precise enough for frame making.
And then, after assembly, your frame is square and glued up, you notice tiny gaps in the miter joint. Oh NO! But relax and order a small container of Timber Mate, which comes in the colors of most common wood species on Amazon. Take a tiny bit on your finger and rub it in gently. Sand off the excess and the gap disappears. This stuff also finishes exactly like the wood. For a perfectionist like me, it is the critical final touch. Don't forget to remove any glue squeeze out.
Speaking of glue joints: If you're gluing end grain, carefully apply a coat to each end, let it dry, the add a second coat and press them together. I cover the bench with glossy side up. You might wish to make a corner jig or use a corner clamp to make sure it's square. If you do, wax the heck out of the base so you don't glue your frame to the jig.
Long post, and I hope it is helpful. Making picture frames is a gas!