You are going to have to clarify where these numbers are coming from.

I assume that your 27.25 is actually 27 x 1 1/4 as written on the sidewall?

If any of these numbers are coming from a measuring tape, you need to throw them out and start again with numbers that are stamped on the rim itself (preferably) or the tire sidewall (assuming the tire does fit the rim correctly)

If the tire is a 27 x 1 1/4 then you should use a 700x18-23 tube.

Before installing, check that all spoke nipples are covered with rim tape.

Before installing check the tire for any nails or anyhting embedded.

Before installing, check for any visible holes in the tire including the sidewall

If all is ok, install the tire: WHen you install the tube, inflate it just slightly to hold its shape and put it in the tire, then put the tire on the rim one bead at a time.

Before you inflate, make sure the beads are both fully installed onto the rim. Inflate slightly and then spin the wheel to make sure the tire is not bumping out at any spot - this indicated that the bead is not seated correctly.

Slowly bring up to pressure and you should be OK