The bayou burner and a 10g pot are both reasonable suggestions, especially for someone just starting out who doesn't know if they'll like the hobby or not. The reason I suggested a 15g pot is because there's a rather negligible (imho) price difference ($42) between the 10g and 15g stainless steel pots, and a 15g is something that will have the recipient not feel constrained and needing to upgrade later should they get into the hobby with reasonable enthusiasm. However, the recipient is turning 60, and probably doesn't want to be lugging around heavy equipment, so perhaps the 10g is indeed more appropriate in this case, and many-a-brewers are well satisfied with a 10g pot. So this one's a trade-off and (imho) the OP has two very reasonable suggestions to choose between. Sticking with 10 gallons and using the cost savings towards a wort-chiller is probably the better option.
I also chose to list the blichmann burner over the bayou burner, as the OP suggested that the recipient admires quality over most other considerations. I've never used anything but the blichmann so I can't adequately compare. However, I did do quite a bit of research on the two before buying myself a blichhmann burner, and everything other than cost pointed to it being a better burner: quieter, more efficient on gas, upgradeable (stands of various sorts) and good customer service reviews from other users. By all means though, most reports on here suggest that people are satisfied with the bayou burner with the exception that I've heard of poor customer service if there are problems (which I have no experience of myself). Personally, whenever I'm shopping between two items like this, if I go with the cheaper option then I'm often wondering how much it'd have been better had I gone with the 'better' item. Given the OPs description of the recipient, I would still recommend the blichmann over the bayou, but it's a reasonable suggestion to go with the bayou. The cost savings by going with the bayou would ensure the recipient a wort chiller without going over budget. If it were me though and the budget needed to be stretched a wee bit, then I'd choose the blichmann over the bayou as originally suggested.
I did not recommend a fermentation chamber for several reasons: First, from what I gather the recipient lives in WA state and from what I guess, it's very few months of the year that he's likely to be battling higher than desirable fermentation temps. A simple and cheaply assembled swamp cooler will likely suffice for his needs in those instances. Any brewers from WA can give the OP a more accurate indication of brewing climate though. If he has a basement, then I imagine it's a no-brainer to avoid getting one at this time unless he really wants to do lagers. If he later does find he wants to dedicate money (and space) to a fermentation chamber, then it's an option for an upgrade that doesn't mean money was wasted in the initial purchase.
All in all, it's probably wise to go with the 10 gallon pot, as others have suggested, and with the savings, get a wort chiller. It's the one item when I was making the list that I was regretting being unable to include for cost considerations. I recommend a 25 foot, 3/8" OD (outside diameter) copper immersion wort chiller. Midwestern (the site quoted for the other equipment) has them for about $70, but someone posted a link on here the other day of one for about $45. That would keep you close to your budget, but I suspect with shipping (and taxes?) you'll be a little over. Sacrifice the blichmann for a bayou and you should probably be well within budget.
