So you have some money in your pocket now, time to upgrade your gear!
On the sidebar is a link titles 'explore,' explore lets you acces other features of the game, click on the link titled 'base exchange.' You should now see links to various shops and markets. First you should go to 'barrack shop' and look for a weapon you would like (within your price rangwe of course), then go back to base exchange and search the 'player shops' for the weapon you liked, see if there are any deals better than the barrack shop. Buying here gives money to the shops owner. You should also go to the 'item market' and set up a search criteria for your item.
The same applies to other items such as armor, AI chips, and medical supplies.
You can add something you own to the item market by going to 'items' (on the sidebar) and then clicking "add to market" on the corrosponding item, be sure to get you price right!