I'm looking at getting into fixing old bikes as a hobby, but I'm not sure what basic tools I need. I assume a wrench set and allen key set, but do they need to be metric or standard, or both depending on the brand and year of bike I'm working on? What else would be useful to have that doesn't break the bank?

Most bikes are metric. In fact, you'll be surprised at how much you can do with only a 5mm allen key. As you get more into it, you will find that you need some more specialized tools but what you need will depend to a great extent on the particular bike that you're working on and it's age. Honestly, my recommendation is to start with a decent quality metric allen wrench set and acquire other tools as you find that you need them.

I think you'll need a good cable cutter go to Parks or Pedro , maybe a crank puller that's handie , whole bunch of other tools that you'll need when you need them, you'll know then

Crank puller is nice when it's time to service the bottom bracket. I'd also grab the appropriate freewheel wrench (older bikes have them but you may have a cassette and will need the cassette lockring tool instead). Cone wrenches are great for working on the hub bearings.

You sound like a great candidate for a tool kit. :-)

Why not head over to one of the online bike stores and check them out?

It depends A LOT on the particular bike(s) you're working on.

General tools:

• Metric hex (Allen) wrench set.
• Metric wrench set, especially if you're working on bikes from the '70s or older.
• Screwdrivers, mostly for older (or lower-end) bikes.

Bike-specific tools:

• Cable & housing cutter.
• Chain breaker, for shortening new chains and/or rejoining old non-peened ones.
• Chain whip for removing cassettes.
• Freewheel/cassette lockring tools for the particular bike(s) you'll be working on.
• Bottom bracket tool(s) for the particular bike(s) you'll be working on.
• Crank puller if you'll be working on square taper or splined cranks.
• Pin spanner and bottom bracket lockring tool if you'll be working on cup-and-cone bottom brackets.
• Big-@$$ wrench(es) for bottom bracket fixed cups and/or lockring tools. (I find a 15" crescent to be handy.)
• Cone wrenches if you'll be servicing cup-and-cone wheel hubs.
• Headset wrench(es) if you'll be servicing threaded headsets.

...and I'm sure I'm forgetting a thing or two.

Like Retro Grouch said above, start a metric hex (Allen) wrench set is an important start. Past that, it depends on the specific bike(s) and the particular work you need to do, so add tools as needed.

Other than a few universal basics, like Allen wrenches; a chain tool; and cable/housing cutters, you're better off waiting till the need arises before getting a bunch of tools. If you buy a kit or get a bunch of tools in anticipation, you'll likely still find that you don't have the tools you need for a particular job, and have to end up getting more, anyway.

A lot of tools which you might only have a need for on rare occasions, can be improvised- like a headset press. Rather than purchasing a tool you might only use once every ten years, always google around for alternatives....you'll often find lot of good ideas out there in cyberspace.

And of course, if you don't already have 'em in your bag-O-tricks, the requisite pair of Vise-Grips (Regular; small; and needlenose, if you really want to be prepared) are always life-savers, for working on anything!

And a magnet on a stick, for finding lost little parts/fasteners that you've dropped......