Sun Dolphin manufactures one or two 10' sit-on-top kayaks for under $350.00. I know they would be suitable for a day of recreational paddling on a calm lake or river. But could they reasonably be used (with or without modifications) for a solo camping trip of 2-3 days with the same lake/river conditions?
There's no reason why a boat of this type could not be used for short expedition type trips, assuming you stay within the capabilities of the boat and paddler.
As boats of this type don't usually have watertight hatches you need to consider a couple of things, importantly
- Securing your gear to the boat
- Ensuring your dry gear stays dry
10' boats don't tend to be especially fast in the water, so don't expect to be going long distance, but they should be perfectly capable otherwise.
Most boats also have a design weight range, consider this when purchasing as it affects how much gear you're able to take on your expedition. An overloaded boat will wallow and be unstable. Larger boats tend to have a higher weight limit, as 10' is reasonably small you may find you're limited for gear.
Just wanted to second the comments above about keeping your gear dry. If it’s within your budget, good-quality drybags will be good for this and all future adventures. But extra-large ziplock bags, kitchen trash compactor bags, or just ordinary trash bags closed and handled carefully (put inside duffels to protect them from rocks etc) will work. Does your expected weather make a wet sleeping bag a comfort issue or a hypothermia issue?
Regarding canoe vs. kayak: The main virtue of a kayak is its ability to lay low beneath wind that would blow a long high-sided canoe off course and survive waves / wind chop that would swamp any open boat. They’re also a little more intuitive for a novice to steer. If you know your route is flat and calm a canoe may be a great choice, you can pack luxuriously and spend your time paddling not packing and unpacking in little bags.
Regarding price: You may also consider a used touring kayak with hatches and a rudder that you sell after the trip, or when you want to upgrade, for exactly what you paid ($500-$1500). Kayaks that already show moderate wear and tear don’t seem to further diminish in value very quickly.
In all of these cases consider storage and transport. A 10’ boat is easier to contend with off of the water, and will get there eventually.
Regarding sit on tops vs. sit-inside: Sit on tops offer a safety benefit in warm water and moderate wind in that if you capsize they don’t flood, you just scramble back on. A sit-inside kayak is moved less by wind but merits plenty of practice getting back in and pumping it dry after capsize unless you are absolutely certain you’ll stay so close to shore you can just swim to the bank with it.