Napalm
I think your bike will be more that adequate for the tour.
As you said, tyres and tubes will always be available for 26" wheels, and compared to a larger 700c road bike wheel, it should be stronger for those rough roads.
As far as panniers go, the consensus is that Ortlieb is the way to go, so good choice there.
I would recommend fitting as many water bottles to the frame using the existing mounting holes and these (they are strap on mounts for additional bottle cages) http://www.parker-international.co.uk/53/Elite-VIP-Bottle-Cage-Clamps.html, just to allow more room in the panniers so you can either pack more, or make everything inside more accessible/less packed in.
I cannot emphasise enough how important handlebars are. After many miles with your hands in one position, they start to hurt. You want to be able to move your hands to different positions for relief. I would recommend butterfly bars because they offer an infinite amount of hand positions and unlike drop downs you do not need to get new brake levers or gear triggers (and with drop downs, you will never really use the bottom position while touring- too uncomfortable). Get thick padding as well (not just thin bar tape!)
One last thing, mudguards! They are a much needed accessory because it stops your feet, back panniers etc from getting soaked. Try to use a rear (longer) mudguard on the front and have that mudguard set so it is close to the floor and also extends up past the exact top of the wheel to stop spray drenching your feet and to stop forwards travelling spray getting blown back into your face by the wind respectively.
Actually I lied, on more thing. Use clipless pedals. Most tourers use MTB clipless rather that road clipless, because MTB clipless shoes are easier to walk in. I like shimano M520’s, they are very good, simple, tough and cheap. And get some overshoes for your clipless shoes otherwise your feet will get soaked in the rain.
Oh and bike lights- since your on a budget, get a Planet bike superflash for the back (aka smart superflash)- they are very highly rated within the cycling comunity. For the front, lot’s of people are mounting torches instead of dedicated bike lights, simply because of better bang for your buck, or should I say better lux for your buck.
As far as technique goes, a higher cadence is more sustainable (80-100). If you want to know why just ask me, because this post is quite long already lol. And eat and drink lots. And wear lycra. And get a cycling computer.