Hi there, I've got an old Shimano front derailleur that needs replacing on my bike, its only labeling says 'Shimano 105.' The bike has two rings on the front, Shimano 600. It has a mounting piece built onto the frame which I'd like to keep using (pictures below). Can anyone please recommend a replacement, preferably relatively inexpensive, and available to purchase online! Thank you, and if you need any further information please let me know.

How many speeds? (2 in front, how many in back?) Chain width varies with number of speeds, and I just want to make sure we recommend a derailleur that's ideal for your chain width.

But speaking in generalities... Pretty much any indexing-compatible Shimano front derailleur made for standard double chainrings should work.

To give you a ballpark example... A Shimano Sora 3500 braze-on derailleur for a 9-speed (2x9) drivetrain and standard chainrings sells for about $20-25, brand new from Amazon. Sora's not a high-end groupset, but they're decent parts for the price. If you want something more midrange like 105, you can probably go there without spending a fortune (but you may have to go used or new-old-stock depending on the number of speeds in your drivetrain).

It's actually a 5 ring cog on the back, but the bike is a sort of throw-together from a used bike shop, so to be honest I doubt that either the Shimano Ultegra derailleur or the Shimano 105 FD are appropriate for the setup... Do your recommendations still stand, or would you suggest something else? Thanks for the help.

5 cogs in the back? You're almost certainly using friction shifting, which means pretty much anything will work. Well, so long as it's a braze-on derailleur in this particular case. Derailleurs made for fewer speeds may have slightly wider cages to accommodate chains made for less cogs (and making for less chain rub when cross-chaining), so I'd personally try to shoot for 8-speed or lower.

Here are a few new derailleurs that'll work for you:
Shimano Tiagra FD-R440 on eBay, $14.60 with free shipping from Taiwan
Shimano FD-2300 (Claris) on eBay, $11.97 with free shipping from Minnesota
Shimano Claris 2400 on Amazon, $18.27 with free shipping

eBay has plenty of used ones in varying condition. I'm a little hesitant to suggest one in case I happen to pick a lemon or a bad seller, but there are LOTS you can evaluate yourself and choose from. There are a few braze-on Shimano 105 FD-1050 or FD-1055 derailleurs which would be a great fit. Shimano 600. A few SunTour models.

Thanks a ton for this information, very helpful. I'll pick up one of your recommendations.

Literally any Shimano braze on derailleur from 1985 to now would do just fine, since you're friction shifting it. Right now new 5600-5700 series units are a great deal, I picked up two of them for under $20 each recently and one of them was new.