You'll likely get some competing advice, and have to make some decisions. Here's my take after reading what it appears you intend to do. You're on a forum here for ultralight backpacking, which is a specialized activity, but your trip has some special needs which will not always be ultralight. I spent 9 months hitchhiking, freight train hopping, and stealth camping around the US a few years ago. I think that is somewhat more similar to what you'll experience. Varied climate, season, and both rural and urban camping.
First, it seems you won't really be in extreme winter conditions. Save a few bucks and don't sleep at the top of the Andes in a blizzard, it's not safe with minimal experience and it will make gear choices much easier. Also, judging by your previous comments, it seems that you need gear with these criteria: 1. Durable...you'll be using it daily for a long time. 2. Easy and simple...you're new at this and will be in a range of as yet unanticipated adventures. 3. Flexible...jungle, mountains, urban, different seasons, etc. 4. Price...save some bucks for your adventures.
OK, that said, here are some general recommendations:
1. Tent. Go with something durable, easy (freestanding) and packable, that doesn't cost too much. The REI tent ideas are excellent...durable, relatively cheap, and a forever guarantee. I might suggest the 1/4 dome or the flash, but the Passage 1 would also be a good option, it's a bit heavier but more durable, cheaper, and is green, the better for the stealth camping I suspect you'll end up doing at some point. A 1 person tent will be plenty for you unless you are traveling with a friend.
2. Sleeping bag. Here's where I'm going different than others. Get a water resistant down bag (marmot plasma, rei flash, marmot helium, Kelty Cosmic down) but get one that is lighter weight and rated for warmer weather (30-40 degrees). That will cover you in most of your situations. Add to that a good sleeping bag liner (such as: http://www.rei.com/product/797112/sea-to-summit-insect-shield-coolmax-adaptor-liner-mummy#descriptionTab). That will give you another 5-8 degrees of warmth when needed, and will work instead of the big bag in hot weather. So now you have options, based on weather...no bag, just liner, just bag, bag+ liner, bag+liner+ warmest clothes. You should be good down to a little below freezing. The liner gives you the extra advantage of keeping your bag cleaner, the liner being much more easily washable. Let me add one more thing here. I know you already have a sleep pad, but you might consider adding a closed cell pad like a thermarest zlight or solite. They are cheap and indestructible. I'm skeptical that any inflatable pad will survive a year in the conditions you'll be in.
3. Stove. Keep it simple. Snowpeak gigapower is the easiest to use, as long as you'll have access to canisters. Again, I don't see you in much below freezing weather, so cold weather stoves are a non-issue. Light, cheap, durable.
4. You haven't mentioned a backpack, but it's a key piece for you to consider. For this trip, DO NOT get an ultralight bag. You heard me right. Get a tough, durable, comfortable, supportive, preferably water resistant bag. It WILL fall off a bus in Guatamala, get crammed under 1000 pounds of luggage in Panama, get rained on in Peru for 5 days straight, and you'll sit on it every 10 minutes. Don't scrimp on the bag. Maybe Gregory, Dueter, or Arc'teryx would be a good choice. In any case, go to REI or wherever, try on a bunch, get one that is large enough, fits you perfectly, and has a very durable, water repellant construction and a substantial hip belt. These will weigh a bit more (3-5 pounds) but for the kind of trip you're doing, it seems essential.
5. Shoes/boots. Another really important consideration. For a trip like yours, I'd suggest a pair of comfortable, tough but light boots. Something that breathes and dries quickly. Then bring along a light pair of shoes/sandals for when you aren't carrying the bag. Forget waterproof boots. Quick drying will serve you better. Even classic leather might be ideal for your trip.
OK, let the flaming begin. I know folks here love ultralight gear, and it has a place and purpose. But I think the specifics of your trip demand thinking differently. Get the lightest gear you can...but that is reasonably priced, meets your needs, flexible, and most importantly will survive 18 months of torture.