If your trainer hasn't got any sort of remote (like the cable I have running to my handlebars) then you will find it best to change bike gears while riding. Just avoid the combinations like small ring up fron & small cog up back or big rigng up front & big cog up back as these combos are bad for your chain (stretch & wear).

I have a remote lever to change the mag resistance on the trainer, but honestly I find that I use my bike gears more and it helps to produce more of a real riding feel than just adjusting the mag resistance on it's own. Although you will have to find the best (out of 5 settings available) for your fitness level at to start with, and adjust in accordance if you need a harder workout etc.

I remember reading somewhere too that pro riders do use a specific routine on the trainer with specific gear combinations for specific lengths of time to train in ceratin aspects of performance or fitness (cardio, or power etc).

And don't worry about having a limited budget for the bike, sometimes I wish I had brought a cheaper model trainer than I did because I think it would have done just as good a job

The rear tyre is exactly the same to change as the front - only it can be a bit confusing when putting the wheel back on - so take good note of how it sits with regards to the rear derailleur and while you are removing it. I still find that I have to pay good attention to that aspect even now!