I've only been playing the application game for a few years, but here's my nutshell version (I'm sure I'll get some of this wrong...going mostly off of memory). There is a ton of information to digest when discussing all states and all species. Publications like the Huntin' Fool devote multiple pages of information to each state, so there are plenty of details a nutshell version will leave out. Here's some things I've picked up though.
States that charge up-front: New Mexico, Colorado, Wyoming, Montana, California (deer)
States that don't charge up-front: Arizona, Idaho, Washington, Oregon, California (all other species), Washington, Utah, Nevada
States requiring you to buy a license up front: New Mexico, Idaho, Oregon, California, Nevada, Arizona, Utah. Licenses are typically in the $150 range for Idaho, Oregon, Nevada, California, and Arizona. They are typicall $60 or so in other states. In many states, once you buy a license it is only a bit more to apply for each species and it's recommended that you do it.
Generally non-refundable application (ie, not license) fees are typically $10-20 in most states per species.
The point systems and tag distribution for residents and non-residents is very different state-by-state. I'm not even going to get into the allocation, but you really need to research which state it's even possible to draw a tag in and which state isn't (it's different depending on the unit in most states).
Arizona, Colorado, Wyoming, Utah, California, and Oregon (deer, elk, and antelope) all have some sort of preference point system in place (some giving a % of tags to the highest point holder, some giving all the tags to the highest point holders).
Nevada, Washington, and Montana have a bonus point system in place. Each of these states has implemented a bonus point squared system.
Idaho, New Mexico, and Oregon (sheep) have no bonus or preference point system in place. Your odds are the same as everyone else each year you apply.
In the limited units, it is possible to draw in Idaho, New Mexico, Oregon, Nevada, Washington, Montana, Wyoming, and Utah (although the odds in some of those states and units is extremely low without bonus points). It is impossible to draw the top units in Colorado the first year you apply.
Colorado, Nevada, Wyoming, and Utah are must apply for states for deer. Arizona, Colorado, Nevada, Utah, Wyoming, and New Mexico are must apply for states for elk. Apply for ALL sheep tags you can. Idaho you can only apply for one once-in-a-lifetime species (moose, goat, sheep) or one of elk, deer, antelope (you cannot apply for goat and sheep in the same year, or goat and deer, or deer and elk for example). I haven't really got into the moose or goat game in any state, but my recommendation would be to apply for all of those tags you can if you are interested. These last few sentences are just my opinion.
As far as points required it differs greatly amongst states, units, and species. Some take upwards of 20 points, some tags you can draw with zero as I mentioned before. It's really hard to answer that question without doing a detailed state-by-state, unit-by-unit breakdown.
Hope that helped some. My bill last year for all of my applications was somewhere in the neighborhood of $20k. Non-refundable license and fees were probably around $1,000 or so.
