In general, ore is the most valuable resource, followed by brick (with obvious caveats about this not being true in all situations).
This conclusion is based first and foremost on the trade ratios I've observed over dozens of games. Ore and brick are most likely to command multiple resources in trades from other people and least likely to be used in trades with the bank. Using a 2:1 ore port is so rare that there should be an achievement for it.
For a more quantitative angle, we can put relative prices on the various resources by means of a supply and demand analysis. Supply is simple: count the pips. You already have that in your question: 13 for wood and wheat, 12 for sheep, and 10 for brick and ore. This is fairly representative of the average supply, as there are only 3 brick and wheat tiles but 4 of the other three, though supply can deviate substantially from this in a random map.
In order to get numbers for demand, we have to know what resources people want. There are two typical strategies that will win in base Catan: wide and tall. Wide means building a bunch of roads and settlements; the strategy wins with something like longest road, two cities, and four settlements although there are plenty of other variations (a single VP objective card helps a lot, especially if you can't get longest road). Tall means focusing on cities and development cards; this typically wins with 3 cities, and four more points from some mix of largest army, VP development cards, and a fourth settlement/city.
To get hard demand numbers, we need to make a few assumptions. Let's assume we have three players, with two of the players going wide and one going tall (the reason for three players is that 2:1 is a fairly typical ratio of wide vs tall strategies in my experience). The wide players each want to build 7 roads, 4 settlements, 2 cities, and 1 development card. The tall player wants to build 2 roads, 2 settlements, 3 cities, and 6 development cards. Thus, the wide players each want 11 brick, 11 wood, 9 wheat, 7 ore, and 5 sheep, and the tall player wants 4 brick, 4 wood, 14 wheat, 15 ore, and 8 sheep.
This gives us the following:
|Demand / Supply
Obviously the value of resources is situational; if you are at 9 points and are just missing a sheep to build a final settlement and win, then sheep is the most important resource to you. Different boards and players can also change the values, both in changing the numbers in the supply column (which is straightforward), but also in changing the demand column based on the strategies players are pursuing. These numbers are meant to be illustrative of what resources are "typcially" worth; a baseline price if you will. It's easy to see that the price a player would pay in a particular situation can deviate from the baseline price because no resource is worth more than twice as any other at baseline, but players regularly use 2:1 and 3:1 ports throughout the game.
The value of resources also changes throughout the game. Brick and wood are more valuable early game than late game because in the early game is when you may be racing other players to claim key road or settlement spots. Meanwhile, wheat and ore are more valuable late game, because uprgading your main cities (and keeping the robber off of key tiles) is better for your production than builing in one of the remaining marginal settlement spots. Here again, player preferences and the board can change things. One of my favorite openings is to take a high value ore spot with a starting settlement and have my first purchase be a city upgrade (as the starting settlement spots are almost always the most productive spots in the game), but this play only works on some boards.
Unintuitive Nature of Results
The value of ore is often surprising to new players because you don't "need" it at first. You can play the opening, getting purely roads and settlements, without any ore. Thus, there is a temptation to go for starting locations that give you a good spread of non-ore resources, under the thinking that you can pick up ore later. The problem is you can't win without ore; you can get at most 7 points (5 settlements and 2 for longest road) since you can't build more than five settlements without upgrading some to cities.
Cities in particular are massively ore intensive; getting shut out of good ore production is almost always fatal in the late game, as even with a great 2:1 port setup, you're going to be missing out on key trade opportunities with other players who are hungry for ore and willing to trade at quite favorable rates for it later.
Ignoring a high-value (5 pip) ore tile in the opening can be catastrophically expensive later. If someone else can build the easy settlement spot on that tile as a starting settlement or beat you in the race to that tile, your recourse is usually to build several extra roads just to get on the tile at all (usually in a worse settlement spot) or to settle for a less productive (2 or 3 pip) ore tile.