Along with a welding machine of your choice, Wire feed or Stick weld (I recommend both if you can afford it)- you can get as exotic as your wallet allows here, you need a good welding table, the bigger the better but make sure it matches your work shop area. No need to get a 4 x 8 table if you dont have room for it and the rest of your required equipment. Invest in a good auto-dark hood, some good leather welding gloves (TILLMAN make great gloves) and sleeves if stick welding otherwise a good heavy cotton shirt. I also recommend a bandana for neck protection from the UV light.
With a light weight inverter machine, invest in a portable cart for it and some tools rather that just setting it on your work table. Invest in some good grinders because you will need them. I recommend at least 4- one with a hard disc , one with a flapper wheel, one with a cut-off wheel and one with a wire brush. I have 3 of the higher quality HF blue ones plus 2 Dewalt. I also have 7" HF that has worked fine for many years.
One thing I just found at HF that works really well is the 7" cut off wheels on my 7" grinder. You can cut much large with the 7 compared to the 4.5 and you wont have as much waste. When it gets too small for the 7" you can use the rest on your 4.5" grinder.
Many folks seem to use only a plasma cutter to do everything but I find I still need my oxy-acetylene rig occasionally. It sometimes works better than the plasma especially if you need to cut something up in a corner. You can cut practically flush to a corner with a oxy rig but not less than 1/2" with a plasma. Another plus with an oxy-acetylene rig is that you can also braze and weld with it.
TIG welding is also a fun thing to do with welding. You can do all sorts of things with a TIG welder. SO after you master Stick welding, MIG welding and oxy-fuel welding, try out TIG welding.