No need to spend much if funds are tight. A long seatpost can be purchased quite inexpensively. Since you're looking at eventually replacing this bike I'd opt for a cheap basic seatpost - just be sure it's the right diameter for your frame.

And I'd be very surprised if there's any problem mounting narrower tires on your current rims. If your rims are about an inch wide then 1.25" tires or even 1" tires should work (but I'd stick with 1.25" to avoid pinch flats and having to pump them up before every ride).