You definitely want to check all the belts and hoses. Make sure the belts are tight and don't show any signs of rotting like frayed edges and stuff like that. Look up on YouTube or Google images to see what they should and should NOT look like. Out of your hoses, especially check the one going into/out of radiator--up near the front usually. If that goes, shell loose all the water, overheat and the block will crack. (I've been there, done that, and got the T-shirt.And it SUCKS.)
Other than an oil change--which is definitely a must--take it easy for the first 100 or so miles and the first few weeks of driving it. Especially when the engine is cold at start up. Don't go over 55 or 60 mph during that time.
Check all other fluids too: windshield washer levels, water level in the radiator and its overflow (also make sure she can handle the temperature. I don't know where you live but find out what temps it should be able to withstand and mix the water and antifreeze/coolant as per instructions, Ideally you should do a flush and fill too, but that can wait if the mix in the radiator looks clean and clear (should be a see-through greenish color, not cloudy.). Check the brake fluid--be VERY careful when checking that. You don't want to get ANY dirt or crud in there. Wipe any dust or dirt off the master cylinder cover before opening it to look at the level. Add a little at a time if needed. Don't overfill. Make sure you use the right type. If you aren't sure ask the guy or girl working there; any auto place personnel can look it up on their computer.
While you're at it, you might as well check the tranny fluid level too. You'll want someone to help. Start it up and let it run at idle until its warm (normal temp). Then shift slowly through each gear with your foot pressed firmly down on the brake the entire time. NEVER shift without your foot on the brake pedal. For this use both feet--in case a friend is standing in front of the car you want to be really safe rather than really sorry. Of course, check the battery cells and fill as needed to fill lines inside cells (you already said you would clean it) unless yours is a sealed, maintenance-free type of battery.
I can't think of anything else off hand. If I do I'll get back to you. Always repeat those checks periodically, especially the first few months you're using it. I'd check the oil and water every week or twice weekly for the first month. Keep checking those levels, and any hoses, to make sure you aren't burning or leaking anything anywhere.
You'd want to do that with any car, even if it wasn't sitting for a few years. Just maybe not so often. She may feel a little 'sluggish' at first but that's to be expected. Whatever oils and other fluids were in there have settled deep over time. They're far from where they should be and they need to return and reabsorb & re-coat all the little cracks and crevices inside all those moving parts. Be patient and she'll loosen up in time (probably by summer, when it counts).
As for the tires, they might have been brand new four years ago, but rubber rots, in dry or damp areas. Make sure the air is at the proper psi (usually somewhere between 28 and 32 for passenger cars). The correct pressure will be listed on a tag either on the inside of one of the door panels (passenger generally) or B pillar (the separating beam between the front and rear seat of the car [unless it's two door, but I don't think Camry has a 2-door]) or, in the Camry it's sometimes inside the glove box.
Always fill them when they're cold if at all possible. Driving causes friction that heats the air in the tires. This makes the air expand, thereby increasing pressure against the tire wall, and gives a higher than normal false reading. The measurements you take when they're cold is the accurate true psi measure.
Also, keep in mind that a lot of engine parts have rubber seals and/or gaskets, and these will rot too. If you can't take them out or replace them you can temporarily swell them with stuff called "belt dressing". That's actually just a hydrocarbon in spray form, like ether, ad it gets absorbed by and swells the rubber seal or gasket. But it's only a temporary fix.If something is leaking it eventually must be repaired or replaced.
Also you should change the the engine air filter, and maybe the fuel filter too. The first is extremely easy and the second is pretty easy also though not as easy as the air filter. There's a cabin air filter that a lot of guys tell you to change. It runs about $65 to $75 installed, though it costs about $25 to buy and put in yourself. But I personally think it's a total waste of time and money. Unless there's a lot of heavy smoking going on in the car, don't worry about it now (or maybe even ever).
As for spark plugs, if the car isn't showing any signs of fouled plugs: hesitation, hard starting, running rough at idle, I wouldn't bother,. They're most likely platinum and good for another 35 or more thousand miles. If you want to be sure, pull just one and compare it to pictures on line to see if it looks like it needs to be replaced. If it looks clean and there's no gunk or deposits built up on it, it's most likely just fine and you can get on with the other stuff.
All together that should have you more than ready to run. Just remember to treat her like she's a brand new 'baby' (after all, to you she is) and with a little tender loving care she'll be fine.
The Camry is a really good car and she should give you at least another 200 thousand miles or more. Just that engine w just 55 K miles on it alone is worth more than most of the cars my friends have. Even the four cylinder Camry has remarkable "get-up n' go" compared to her American 'cousins'. Do your periodic maintenance as scheduled: oil changes, tune ups, etc. and she won't let you down and you won't want to ever let her go.