Reliable food source?
Well, maybe the usual spot for your base is in the wrong place then. If you simply can't reach food from there, find a place where you can.
Rabbits are pretty good early on. Berries are good, as you mentioned, but aren't going to be enough on their own. Forage for them early on, but later you should dig them up and move them to your base.
If you see a bird, move towards it to scare it off -- they drop seeds at a decent rate. If you are still in a starvation situation, eat the seeds, otherwise you can combine them with manure to start farming.
Monster meat is edible, but it does damage. Early on, if you are having trouble getting enough food, keep in mind that you can eat monster meat at full health followed by a couple berries. Over the next couple days, regular eating should heal you up enough to recover to where you can do this again if need be.
Getting manure for farms will help, but since it still takes a seed and farms grow pretty slowly, this probably won't solve all your problems.
Tallbird eggs are amazing, if you can find them.
All food should be cooked before you eat it -- it will go a lot further this way.
Throughout the game, but especially early on, keep in mind you will need to rely on many types of food source. Always keep an eye on your map for berry bushes. Always approach birds for seeds. Always grab carrots. If you see a rabbit straying from his hole, hunt it. Unless you happen upon several tallbird nests within a comfortable walk of each other, you aren't going to find a single stable food source.
Summer (farms)
Set up near a herd of Beefalo. They'll produce Manure. Use it to make Improved Farms, which you can use to grow crops. This will get you through summer.
Winter (rabbits)
Crops don't grow in the winter. But if you built near beefalo, you're near grasslands with a plethora of rabbit holes. Create traps (you'll need lots of grass and some twigs), and put them on top of the rabbit holes. You can catch one or two rabbits per hole per day this way.
Winter advanced (jerky)
Winter's reduced sunlight leads to reduced sanity. To combat this, make Drying Racks. You can dry rabbit meat on the racks, producing Small Jerky in one day. Each Small Jerky consumed gives you +10 sanity, in addition to hunger and health benefits. You'll need 6 small jerky per day to maintain your hunger level. So build at least six drying racks. If you build more, you won't have to go rabbit-collecting every single day.
Dragonpie: The food for all seasons
The single best long-term food in the game, Dragonpie can be made in the crockpot. For dragonpie success, you'll need a bird cage, a bird trap, a lot of farms (say, 8 or 10), and a crock pot.
Set out your bird trap and catch a bird. (Bait the trap with seeds to catch a bird faster.) Imprison your captured bird in the bird cage.
Now grow crops with regular seeds. You'll get an assortment of fruits and vegetables. Feed any dragon fruits you get to the bird. For each dragon fruit, he'll give you back 1 or 2 dragon fruit seeds, and sometimes a normal seed as well. Now plant all of those dragon fruit seeds, and fill the rest of the farms with regular seeds. Keep feeding the bird every dragon fruit you get until you have enough dragon fruit seeds to plant a full crop and plenty left over. (You can speed up this process by applying manure; two manure cause a planted crop to grow to maturity instantly.)
Now use your dragon fruits to make dragonpie. Put one dragon fruit and three twigs in a crockpot. Cook. In a minute or so, you'll have a food that gives you 75 hunger, 40 health, and 5 sanity; and it lasts for 15 days before it spoils. You only need to eat one dragonpie per day to keep your hunger at a constant level. So if you make ten, you have a ten-day supply of food. In this way, you can even mostly avoid collecting rabbits in the winter. And dragonpies stack up to 40, so you can carry in one slot far more than you can even eat before they spoil.
Other crock pot foods can give you more hunger or more health. For instance, meaty stew gives you +150 hunger, two days' worth, while waffles give you +60 health. But dragonpie gives you the best combination of hunger, health, slow spoilage, and easy availability of ingredients.
Make your base by a field of bunny holes, and make a spear, and some traps. Bring berry bushes back to your base. I'm on day 32 living with the bunnies. Make a farm of berry bushes and plant stuff in the manure and seed farms.
Works great for me! Good luck, and remember, in future updates this game will only get better.