There are three main skill categories in Tekken Mobile: Attack Skills, Agility Skills and Utility Skills. Out of these, I personally believe that it's just the Attack Skills that should get most of your attention, with a bit of attention focused towards the Utility ones. But let's find out more below.

Attack Skills
These are the best, as I have already said and the one you will want to invest most points in is the basic one: the Increases all tap attack damage skill. It only gives you an increase of 0.4% per level which is indeed a little, but it adds up in the long run and becomes very useful. My favorite one to choose since the basic taps are what you will use the most in battle anyway. Another skill to consider investing in is Increases all elemental damage: this gives a better damage boost, but has its own drawbacks. It only increases the damage when fighting with an elemental advantage. This is what you should normally do, but it won't always be possible. So even though the numbers look good, in the long run it might be less useful since you will have to send your fighters into battles without the elemental bonus. All the other attack skills can be somewhat useful in particular situations, but I see no reason why you would invest in them at all. Focus on the two above (or just the first recommendation) and things will be great, in my opinion.

Agility Skills
These are skills related to your Waza cards and I don't think any of them is really worth investing in. They are specialized on different types of Wazas and because of that, they are limited in benefits. However, if you really want to invest in something, I would recommend going for the Decrease stun/guard break Waza cooldown skill for two reasons: the stun Wazas are absolutely amazing because they open up the door to a ton of combo opportunities; and they also have the longest waiting time before they get activated. So if you really want to invest in something, invest in this alone.

Utility Skills
Even though these skills don't directly affect your in-fight performance, they offer some boosts and bonuses and might be a good choice in some cases. I don't think anybody should actually focus on these because the Attack skills are much better in my opinion, but we have one solid option here: Post match shard drops increased: this is a good skill to have because the shards are required to level up your fighters and you will need a ton of them. However, the extra ones that you get as a reward are not really worth the skill point - if you are active enough in the game you will still get there, but you will have to go through more fights. But at least you will have extra skill points to put where it matters and that is the Attack skills.