We have all been there; brand new to screen printing and having only the basic equipment for starting out. Many start out with an entry level screen printing press (probably only 1 or 2 color capability), an overhead lamp-style exposure unit, a heat gun for a dryer (luckier folks may have started with a dedicated flash unit), a couple of screens, and some basic inks and cleaning chemicals. Those of us who stick with it and do quality work should easily and quickly outgrow startup equipment such as that, and face the task of trying to decide exactly what screen printing equipment should be upgraded, and in what order.
Unfortunately there isn't an answer that fits every shop and every situation. But there are some things to keep in mind when considering the process.
I would argue that a quality conveyor dryer should be one of your first considerations for a new equipment purchase. If you have been using a heat gun, a conveyor dryer will likely make the biggest difference in your shop output and overall efficiency. Where you may have been standing over a shirt for minutes using the heat gun, a quality conveyor dryer will keep an even, consistent, and controlled heat across the shirt for the correct amount of time (belt speed). Print, pull the shirt, lay it on the dryer, done.
Next (in most cases) will likely be your manual screen printing press. I have seen some really interesting modifications to existing starter presses to try to repair or give some sort of new functionality, when modest money could be spent on a newer, higher capability screen printing press, and be done with it. For many screen printers, this may mean going from a tabletop or bench model press, to a full freestanding press. Obviously there are considerations of the area you have available as well. Typically this means going from a 1 or 2 color bench type press, to a 4 color 4 station freestanding manual press (and some will upgrade to even more colors). A quality press such as this will usually have an outstanding warranty and be very durably built. An investment in a quality manual press will give you new capabilities, faster production, and more flexibility.
Perhaps lesser on the list but still important are items such as exposure units, screen drying cabinet, washout booth, etc. Certainly all of these have their place in a well run shop. Upgrading your exposure unit may be especially important as they can significantly cut exposure time and exposure errors. Too many shops are trying to scrape by with older outdated units, and it often seems that they are wrestling to get a quality screen burn. Newer exposure technology, such as LED exposure units will serve your business for many years of trouble free service and quality production.
In the end, only your production needs and your budget will determine the best upgrade path for your screen printing business. But when you feel that you are outgrowing your current screen printing equipment, hopefully these general guidelines will stay in the back of your mind and serve as a good base of knowledge.