I am still fairly new to brewing (less than one year), and I jumped head-first into all grain brewing, so I'm only recommending it because I've never done extract.
I only have a few suggestions/considerations to give before you make a final decision.
1. Look, hourly if not daily, at craigslist. You can find keg shells on there for $20-25 and easily convert them to be your brew kettle, AND you'll already have room for more than 10-gallon if you decide you want larger batches. I have recently seen several DIY tutorials for converting the lid you cut off into the false bottom (Side note, I have not looked into BIAB very much, so I am just assuming this will still work.). You may also luck out and find someone selling their old equipment, or even for a burner.
2. Investigate your area for friends/groups/clubs that may be parting ways with old/unwanted equipment, or at the very least, seek out brewing friends who wouldn't mind loaning a piece of equipment to help with your brew day. (Some friends here pitched in together to buy a plate chiller and pump, so I've been fortunate to save money on buying a chiller and use it elsewhere)
3. Wait for sales. My LHBS just had a St. Patrick's day sale and offered 10, 15, or 17% off, and I know several online stores run promotions too.
I agree with everyone else's comments of doing days and weeks worth of research, and yes, sanitation and temperature control (and measurement!) are two of the most important things to understand. Once you've gotten your system down with your equipment, then you can start having fun tweaking and understanding how ingredients change beers.
Although I have yet to brew or ferment in a Texas summer heat, @BigFloyd makes a good point to consider how you are going to ferment. I would recommend measuring temperatures in your closets, cabinets or anywhere else that's dark and closed off to see if you could be able to maintain 60-70 degree temperatures using a swamp cooler. I know a chamber is next on my list.
I know this probably did not answer any of your questions, but hopefully it gave you something to consider.
Cheers