I tend to focus on improving direct capability first if I can, then shoring up defense, then finally working on other faults.
With that first priority in mind, I'd first see what I can do in regards to better weapons, items that improve spellcasting, bonuses to primary stats, etc. Depending on what actions make that particular character valuable.
It really depends on the kind of character I'm playing. If fighter based then I load up on weapons and armor. If Thief then thieves' tools is usually the priority because it takes up so much gold!
As mentioned above it depends upon the character. I make sure to buy the tools of the trade such as thieve's tools first. Then I decide what weapon or weapons I'm going with and buy them. I buy the minimum of basic supplies I need. I then go and buy the best armor I can afford with the remainder of the gold. I don't spend a lot on armor and buy it first. It can be frustrating to have great armor but have subpar weapons or be lacking basic supplies. The well rounded approach is best in my opinion.
Its annoying to see a player buy a whole bunch of equipment but not take a tent, blanket, food, water, stuff for hygiene, etc. I factor those into the game and it hurts when the character does not have it.
Of course, there are kits but sometimes they do not even get those unless I or other game masters make it an automatic process. I personally do not make it automatic, I like to tease if they forget. I do not remind them either and then they are surprised when I check for it.
I like that. If they don't buy the proper equipment then they are in for a rude awakening. It's bad to need to camp with a rainstorm coming and players realize that they didn't buy tents. After that or something like that happens players are usually better in the future with buying needed equipment.