Correct fastener selection is simple on its face, but it can get complicated very quickly. It is also one of the things that can lead shop personnel to greatly prefer working on the designs of one engineer over another- so you will serve yourself well to learn how to not only select fasteners which will do the job, but also make life as easy as possible for the people who have to build whatever it is that you design.
As a young engineer, NEVER forget this: you have a degree, and that's great. It does not, however, make you 'better' than anyone. The guys on your shop floor, or at your vendor, or at your customer, who build what you design are the ones who make the world go 'round. They very likely have decades of experience. Listen to them, and learn. If they challenge a decision you've made, ask yourself why. They may see a better solution than you did. If they are wrong, stand your ground, and explain your thought process to them so that they understand; in doing so, you may see an even better option than than either of you saw initially. If they are correct, make sure you learn from them and make sure they know that you value their input. This is, by far, the most important advice that anyone can give you in the first few years of the job.
With that said, in general, the decision tree for choosing fasteners goes something like this. Follow this and your fastener choices will be correct MOST of the time. You always need to take a step back after your design work is complete, before it is released, and make sure you haven't missed anything, but this will get you close.
Step 1) Choose a diameter
If one mating part has threads, use that size. Easy. If you have two clearance holes, find the hole size. Select the next smallest size fastener (a 1/2" bolt WILL NOT fit in a 1/2" hole- a 1/2" hole means a 7/16" or smaller fastener, etc).
If you see a hole callout with a 'strange' decimal value, this may indicate that the hole was drilled with a metric drill and a metric fastener is needed; convert your SAE dimension to Millimeters, and see if it's a match for a normal metric bolt clearance hole.
For example- 0.432 inches is 10.97mm. 11 mm is the correct clearance hole for an M10 bolt; so that part with a 0.432" clearance hole on the drawing was likely designed for M10 hardware.
Step 2) Choose a style
What type of fastener and head do you want? Is this an assembly without much tool clearance, which would make a socket head cap screw easier to install than a hex bolt or cap screw? Is this a small/light weight component, which might only need machine or sheet metal screws for mounting?
Step 3) Choose a length
Look at your stack-up of parts. Remember that with clearance holes, you will need enough thread on the far side for a washer and hex nut to properly seat; this means a minimum of 1 full thread must extend past the hex nut- if you use a nylock, past the nylon insert, etc. You want to use the shortest fasteners possible- so that your assembly will always be as inexpensive and as light as possible. If you are putting a fastener into a threaded part, in almost all cases any thread engagement beyond 2*bolt diameter is unecessary, so choose your length accordingly.
Step 4) Choose a material and coating
Does your assembly have a unique corrosion requirement? Is it highly loaded (and thus require high-strength fasteners)? Does your customer have a specific cosmetic requirement? Answering these questions will point you at the material and finish type that you need.
Now you have an 'ideal' fastener configuration for your particular application; in order to actually choose and provide part numbers on your BOM, you need to evaluate this choice and make sure it's correct.
A) Is the fastener I have selected easy to install? For example- if you've picked a hex head bolt, is there sufficient clearance around the bolt head AND nut for the tools necessary to actually install the fastener? If you've chosen a socket head cap screw- is there a direct path to the head of this screw so that an allen key or socket can easily be used to tighten it?
B) Is the fastener I have selected one that is easy to buy? For example- you may calculate that a particular application calls for a 1/2" SHCS, with a grip length of 3 1/8". 3 1/8" is not a standard length and will be hard for your purchasing people to find; the next step is to look at what options are readily available in the type/diameter/material/finish you need, and pick from that list. In this case: 3 1/8" length is not common, but 3 1/4" is very common, so choose 3 1/4" length. Now go back and make sure that this longer length does not collide with anything, still has enough tool clearance to be installed, etc.
C) Am I making life more difficult for the installer than I need to? For example- if you're mounting a bunch of electrical switches or pushbuttons, some with metric clearance holes and some with SAE- is there a single metric or SAE size that will work for all of them? Your panel builder will thank you if they can do the whole job with only one tool, instead of having to switch hex keys to hang two different parts which are right next to each other and appear to have the same hole size.
With regard to washers:
In my own practice, I use flat washers under bolt heads for every single fastener application with one exception- a SHCS in a counterbored hole does not get a washer; the clearance hole will be called out as a close fit, with no washer so that at the standard counterbore depth for the SHCS size chosen, the top of the SHCS is flush with the part surface.
For slots: if you put a high strength bolt into a slot, as the bolt is tightened, the face of the bolt contacting the part is very likely to round over the edge of the slot. Providing a washer prevents this. Also, a washer will generally be larger than the head of the bolt; this provides more area for the bolt to clamp against, which you need since much of the bolt clamping area the bolt would have in a normal hole has been removed to form the slot.
Lockwashers: ditch the standard helical lock washers that are common. They are useless, and their are papers and studies aplenty to back this up. Fastener loosening and what you can do to prevent it is a huge topic unto itself, but there are three main points which will serve you well in most situations:
1) By far, the best method to prevent fasteners from coming loose is making sure that they have enough preload. Bolts which are loose will easily become more loose; bolts which are sufficiently tight will stay that way for longer and under more severe conditions.
2) Helical lock washers simply do not work, ESPECIALLY when combined with a flat washer underneath, which is an extremely common configuration. Anyone who says otherwise has their head in the sand. Save your company and yourself time and money and don't spec them.
3) The most common reason for fasteners to come loose is not fasteners turning- it is loss of preload due to creep or relaxation of the parts being clamped. This is one reason for using flat washers everywhere; by spreading the clamping load of your bolt, you make it less likely that your clamped parts will 'squish' out from under the bolt head and cause your fasteners to come loose.