I have not built a robotic arm myself yet, but I've desinged a few in FreeCAD.
The 6DOF (Excluding gripper!) articulated robot arm is the most universal commanly type, but there are some (commercial) robots that add an extra 3rd arm segment. This can be handy for example for installing a dashboard or a seat into a car, where access into the car is restricted because of the surrounding metal of the car frame.
The "palletizing" robots (Based on parallelograms) are simpler and therefore cheaper (quite often just 4DOF) and when you only want to move items in a horizontal plane it may be adequate. The "EEZYbotARM V3" is a nice DIY example of this. This plywood version from fablab ruc:
https://fablab.ruc.dk/robot-arm-v-0-1/ can quite easily be made in bigger sizes (But has a very low gear ratio, see below). Another model of this "palletizing" type I quite like is the uStepper. A lot of the construction is made of standard tubing (Aluminium, or carbon if you like) while the rest is made with a 3D printer, for ease of replication. This one also has a quite low gear reduction ratio though.
SCARA has the advantage that most of the motors do not have to carry the weight of the payload. This type is relatively common for big magazines for CNC machines.
Then there is of course also the stewart platform. It seems to fit the build of (airplane) simulators well, but it's relatively stiff and I've also seen some examples of it being used for CNC milling.
Then there is the Delta robot arm, which is a "simplified" version of the stewart platform, with only 3 DOF. These can be very quick and are commercially used for pick and place of lightweight objects (such as picking up cookies and stuffing them in boxes).
And of course the XYZ cartesian version. These can easily made to custom size by bolting linear stages together. It is also much like most of the commercial CNC machines.
There are some (probably) good books about robotics, but I never looked much into them. I suspect they are easily to generic, or too detailed.
Of all the (quite many) DIY robot arms I've seen, they nearly always have a quite low gearbox ratio, combined with stepper motors. I guess that a gear ratio of around 1:30 to 1:40 will be optimal, and this is difficult in a high efficiency single stage gearbox (both cycloidal and strainwave can do it, but those are expensive). Nema23 motors run quite well up to about 600rpm, and it's nice if your motors can reach this when they move at their maximum speed. Note that if you double the gear ratio, the stepper motor has to run twice as fast, and it's output torque wil be significantly lower (maybe even near a factor or two), but this is compensated because the input shaft of the gearbox only needs half the torqe. The main gain is in higher resolution, and in higher payload capability for slow movements. All robot arms based on hobby servo motors are quite garbage. Too much backlash, low torque, and mostly not enough resolution to control a robot arm properly. I would never build such a robot myself. Using a single hobby servo in a gripper may be acceptable though.
The combination of motor size and gearbox is quite important and has to made early in the design. I've seen too many DIY robots that can barely hold their own weight, or even don't work at all without a significant re-design. You can either do some calculations (which can be inaccurate due to loss of torque for stepper motors at higher rpm, (unknown) inertia and acceleration, and other factors. You can also start with some motor and gearing, and add a broomstick with an (approximated (final arm + payload)) to the end. This can give you an idea if your motor setup is "adequate" for your case quite quickly.
But what type of robot arm you want to design / built is mostly a personal question. For a lot of the DIY projects, the software seems to be a big stumbling issue. Chris Annin does put a lot of effort into software for his (open sourced) AR3. That may be worth checking into. There are quite a lot of youtube video's about building DIY robot arms and the first movements, but more elaborate examples of doing something useful with them, or even fluid motions are quite rare.
For myself I also do not know yet how I'm going to make it. Some of my designs are based on flat wood panels that can be lasercut, other models are designed to be made from steel tubing. Before you decide on a model to build, think of some long term things you could do with it. A lot of the DIY robot arms probably end up in some closet quite soon. A long term use of a robot arm could for example be something simple as a desk (reading) light. Or maybe a (fixed position) microphone or (macro?) photo camera that swings into position as you start some software on your PC.
The "palletizing" / parallelogram based version can be quite nice for this. I'm thinking of making it dual use as a tapping arm.