Which tube will fit a -(700 x 25c) wheel?

The marking on the tire '700 x 25c' means a 622mm diameter rim, with a nominally 25mm wide tire. ('700c' comes from an older French standard for wheel and tire sizes, it's very commonly used to refer to the standard road bike rims and tire size).

Inner tubes fit a range of tire sizes as they are quite flexible. The two numbers denote the min and max tire sizes. A 700 19-25c tube will fit, as will a 700 25-28c. As long as you tire size fit in the range specified you are good.

Note that tires and tubes may also be marked with 'ISO 622' or 'ETRTO 622' These are both equivalent to 700c.

You also need to get a tube with the correct valve stem length. Tubes come with a range of valve lengths to fit different depth rims. The length is not usually marked on the tube but is easy to measure.

The simplest thing to do of course is take the punctured tube to a bike store and simply ask for new tube that is compatible, for a 25mm tire. Or get your BF to buy his own tubes (or learn how to patch them).

Any 700c tube with "25" in the range would fit - assuming the valve stem is long enough.

Deep-rim aerodynamic wheels require longer stems than older-style box-rim wheels do.

A 700 x 18-23c would probably work fine, especially if the tire is a "small" 25. Bicycle tire and tube sizing is a bit of a crapshoot - one manufacturer's "25" can be a a mm or two larger or smaller than another manufacturer's "25". That can be significant for clearance and tube fit. And tubes are more than a bit flexible - obviously.

Flats are also an expected problem, especially with racing-type bicycles. Almost everyone riding such a bicycle rides with a tool kit that can fix at least one flat tire. Such a kit usually includes a spare tube - or two. Because flats happen, and no one wants to have to patch a tube in the rain.

I think you have the hang of the 25 needing to fit into the range of numbers on the inner tube. These numbers refer to millimetres, the width of the tyre, and tubes can be stretched within reason to suit a few different sizes of tyre.

You're right that the 700 x 35-38 tube is way too big. If you chose that one, it would be unnecessarily heavy and the bagginess of the tube would make it more susceptible to getting pinched when the tyre gets mounted. Putting a hole in the replacement tube is never fun.

Now the 700 x 18-23 tube is a marginal case. This time, the tube will be stretching up to and just beyond the size it is designed for, by 2 mm. There is a difference of opinion on whether this is a problem or not. There was even a semi-recent question on this site about whether a tube should be used at the low or the top end of its range and lets just say there are arguments for either case (cyclists can rarely agree on anything). I would certainly use one of these if I didn't have an alternative but I would prefer to have an 18-25 tube so that it wouldn't even need thinking about.

By using an 18-23 or 18-25, when you put a little air in to install the tube, it takes its size and shape without any bagginess and stays out of the way a little better when you mount the tyre.

So yes, it would be best if there was a 25 in the size range of the tube and 700 x 18-25 tubes do exist quite readily if you can track down a shop with them in stock. 18-28 would also be just fine of course.

TL;DR I think you're on the right path, just facing a bit of doubt because you haven't found them in stock yet. That said, 25 mm tyres are very common on road bikes so I’d expect most bike shops to stock a compatible tube, keep looking and don’t be afraid to ask shop staff to direct you or dig one out from the stock room.

A 700 x 18-23c will fit on a 700 x 25c. I got a 700 x 25c tire, and just had my first puncture on my new road bike last week. Stock inner tube is 700 x 18-23c.