As much as you are willing to spend
It really depends on the type of diving you plan on doing, how often, and how far away the dive site(s) are. It is more expensive at first to buy your own gear than rent, but in the end it CAN be cheaper if you buy. A lot of new divers don't know what they need or want in dive gear and tend to 'throw money' at the problem. Been there, done that, bought the t-shirt. So don't invest in gear until you have a good idea what you need. A good way to see lots of different gear is to join a dive club. You can do that before getting certified. Just hang out and get to know people.
Beyond that there is the cost of time. Horses take a lot of time. Will you have the time to dive?
Dollar costs:
Mask, fins, snorkel, maybe booties
OW training costs - don't skimp.
Regulator ($300-1000), BCD (or Backplate and wing) ($300-$1000)
Exposure suit ($50-$2000)
dive computer or depth gauge and bottom timer ($150-1000)
tank (often best to just rent these)
weights and belt ($100ish)
goodies (lights, scissors, knife, whistle, etc.) (will nickel and dime you - start only with what you really need)
Air fills
Travel expenses
Hotel expenses
Dive charters
As you can see the costs vary widely. If you know what you are doing you can get used - doesn't sound like you are there yet.
OK, for me - I own all my own gear and dive almost exclusively off the beach. My expenses per trip are at a minimum: 400 mile drive ($75 in gas), night lodging at the local hostel ($30), air fills x 4 ($3 each at my LDS bought in bulk), parking/entrance to the dive site ($10-20/day).
Add it up and a 2 day trip costs me $138-158 in direct expenses. As for my gear I have a lot from long ago and some more recent. OTTOMH I'm guessing $3000 in the last 2 years and that is getting used, not getting the top of the line and including a GoPro and SeaLife and homemade canister and video lights in the mix. Actually I'm afraid to total it up. Most people will spend much more.
Just figure it is an expensive activity - at least in the beginning.