There are a lot of great answers here, and I apologize if I had overlooked something.
I wouldn't suggest working out while gaining weight, usually the simplest and most accepted way for getting big is 'Bulking' then ' Cutting '. Though it can be done in other ways, I'm not entirely sure what a good plan would be for perusing those ways..
So if you have 10 - 12 months of free time I would suggest bulking first, then cutting with stronglifts 5x5 you can google it.
Although ' Eating more ' sounds like a great way for gains, I would suggest Eating more but in two meals. This method activates the starvation process in your body and causes it to cling on to everything you give it, though make sure everything your giving it to cling to is good wholesome foods, and not just cakes and sugar...
The way to do it would be, skipping breakfast and maybe having a piece of toast or some light carbs for energy to tie you over until the afternoon. Once lunch comes.. Eat a nice heavy share, but remember to chew

. After a nice lunch, try not to burn it all off by running 15 miles, maybe hang out and watch a movie ? or perhaps read a book.. The second meal of the day should be a late dinner, eat well and serve up some second portions if you feel the need.. then sleep; sleeping is also an important part of this diet, it idles the system to a minimal caloric burn.
Make sure to include some good foods in your diet, 10 cheeseburgers does not qualify as basic nutrition

.
If you can, take flax seed or fish oil along with a multivitamin to ensure you're getting everything you need every day.
Sumo wrestlers actually use this method to bulk up months before competitions. and it's really one of the fastest ways to bulk
so, twice a day, heavy lunch, heavy dinner, sleep, remember to take your vitamins, and drink plenty of water.