will the tires properly fit your RIM is far more of a concern than the tube fitting the tire normally you would go with a tube that is sized a little bit smaller than the tire size you are planning to run, not larger. for example, I use 700x19-23 tubes in tires up to 28 or 32c.
Regarding the other issue, if you run a tire that is too big for the width of your rim, you risk sidewalldamage. if you run a tire that is too narrow for the width of your rim, i believe you risk having it roll off the rim in cornering situations. a lot of mtb have gone to narrower rims over the years so you may be fine. Do you know what kind of rims you have?