First cut out hybrid seeds (yes all of them, F1 etc.) hybrids should not be saved for use next year as most are sterile and sometimes you will need to seed 8-10 just to get one to sprout. Plus unless the cross is stabilized (usually takes 6+ years to achieve (most commercial store bought seeds are stable and are marked with germination tested for 2001 etc.) you won't know if you are in fact getting the genetic make up of that variety or if the seed has reverted back to one of its ancestors, which usually happens after the parents. (grand parents and back) Plus most smaller type tomatoes have a more dominate role in a seeds genetic make-up rather than the larger when crossed, but that is another topic. To avoid the hassle and guess work since we are going after growing giant tomatoes, lets just avoid hybrids.
This leaves all open pollinated or heirloom type seeds left, next narrow it down further to the big ones, like beefsteak types. Here are some you can choose from (listed below) and a little info on each which was supplied by Heirloom Seeds. Just keep in mind,
BIG RAINBOW - The large 1 to 2 pound, deep orange fruits on this variety are covered with beautiful red streaks and spots. The firm, low acid flesh has a delicious flavor, while the large vines provide plenty of leaf cover. Indeterminate vines.
BRANDYWINE (Sudduth's Strain) - From the legendary Ben Quisenberry collection, Mr. Quisenberry obtained this variety from Dorris Sudduth Hill in 1980, who's family took pride in growing for over 80 years. This large, pink beefsteak variety is considered by many to be the best tasting pink tomato. The luscious fruits can weigh up to 2+ pounds and have an intense, rich tomato flavor. Indeterminate vines.
BRANDYWINE, PINK - Introduced in the 1890's, the large vines have potato-leaf like foliage and pink fruit that weigh 1.5 pounds or more! The slightly lobed fruit is mild and juicy, with a low acid taste. Indeterminate vines.
CUOSTRALEE - A great tasting French heirloom variety! Large, beefsteak type tomatoes can measure up to 4 inches across and 3 pounds in weight. The flesh is a beautiful red color and is simply delicious! A very heavy producer! Indeterminate vines.
CRIMSON CUSHION - This old time beefsteak variety has fruit that is deep red in color, ribbed, and weigh 1.5 to 2 pounds each. Rich, tomato flavor! Indeterminate vines.
DELICIOUS - These large, red, beefsteak tomatoes can grow to over 1 pound each, with many growing 2 to 3 pounds! The smooth, solid fruits are crack resistant and meaty, with a small seed cavity. Excellent flavor! Indeterminate vines.
GIANT BEEFSTEAK - This very heavy producer of large, brilliant red tomatoes has been a favorite for years! The solid, meaty fruits are 12 ounce to 2 pounds in size, and are excellent for slicing. Indeterminate vines.
GIANT BELGIUM - The 1½ to 3 pound fruit on this fine tomato plant has a sweet, mild, low acid taste. So sweet, some folks make wine from it! The tomatoes are a deep pink in color and very solid. Indeterminate vines.
GOLIATH - A favorite that dates back to the late 1880's. Largest fruit of any standard variety! This fine flavored, solid tomato produces pink fruit that average 1 - 3 pounds in weight. The perfect tomato for canning or fresh use! Indeterminate vines.
HILLBILLY - This old heirloom variety originally came from the hills of West Virginia. Huge, beefsteak type tomatoes average 1 to 2 pounds, and are yellow-orange in color with red and pink streaks. Mild, low acid taste. Indeterminate vines.
JEFFERSON GIANT - This old heirloom dates back to the 1880's, This exceptionally flavored tomato is heart shaped, pink, with few seeds, and weighs 1 to 2 pounds. Delicious! Indeterminate vines.
KELLOGG’S BREAKFAST - This West Virginia heirloom is orange beefsteak tomato. Truly outstanding taste! This very productive variety bears fruit that weigh 1 pound or more. Indeterminate vines.
MORTGAGE LIFTER - This old, Amish heirloom tomato grows huge (2 pounds or more), pink fruit, that are very meaty and has few seeds. Folk lore states that a farmer sold these tomatoes to pay off the mortgage on his farm! Indeterminate vines.
PONDEROSA - This heirloom was first introduced in 1891, and produces very sweet, pink, meaty giants that weigh 1-2 pounds each. Old fashioned flavor with high yields! Indeterminate vines.
POLISH - This potato leaf foliaged plant produces large, 1 to 1.5 pound, brick red, meaty, irregularly shaped, ribbed fruit. Originally smuggled out of Poland to the United States on the back of a postage stamp! The exquisite flavor of this variety makes it good for either using fresh or for canning. Indeterminate vines.
SCARLET BEEFSTEAK - The bright scarlet colored fruit of this variety can weigh up to 1 pound or more! Very solid and meaty inside with great tomato flavor. A favorite of home gardeners! Indeterminate vines.
SCHELLENBERG'S FAVORITE - This old heirloom from the Schellenberg family
near Mannheim, Germany, produces huge, beefsteak type tomatoes that weigh 1 - 2 pounds each! The oval shaped fruits are red-orange in color, smooth, and resist cracking, a common occurrence in other beefsteak type varieties. Indeterminate vines.
WATERMELON BEEFSTEAK - This fine heirloom dates back to the late 1800’s, and still produces heavy crops of tomatoes that can weigh up to 3 pounds each! The pink skinned fruit has mild, purple-red flesh, and is oblong-shaped, similar to a watermelon. Indeterminate vines.
Note:* There is also T&T Monster, Braggar, Dinner Plate, and Big Zac not listed. These are as well fine variety's to try, Even though Big Zac created by Minnie Zaccaria is a newer cross bred tomato(Hybrid) it looks as though this variety is stabilizing, after all that is were all variety's started from, cross-pollination, but again that is another topic.
These are just some of the best of the big ones, listed above. If I was to rate the top 7 it would look like this. (below in order, with explanation)
1) Delicious (currently holds the worlds record at 7 lbs. 12oz. grown by Gordon Graham of Edmond, Okla.) I don't believe the full potential of this variety has ever been achieved and as well it is one of the best crack resistant beef stakes out there, we will see allot more of this one in the future.
2) Mortgage lifter This is as close to first as it comes, with it being one of the most tried, there are currently over 20 different strains out there so be careful. I personally like Estler's and Radiator Charlies strain. If not for these it would probably come in third to fourth.
3) Goliath This is a solid very large variety and again I don't believe it has been grown to it's potential, it should grow 5 and 6 lb fruit easily.
4) Giant Belgium Hmmm... I couldn't decide here to much like Goliath, only reason it's not third is last year it missed by 4oz. to Goliath.
5) Watermelon Beefsteak Consistent 3-4lb fruit brings this in at number five
6) Big Zac I like growing this one, again consistent at about 4lb fruit, should move up in ranking next year once germination rates improve.
7) Cuostralee This has good potential and should as well move up in the next couple years with a more aged strain.
Well there you have the top seven, there are probably allot more but from my experience these are the crem de la crem.
As well for you that are wondering, my plants average fruit from 3-5 lbs each, constant year after year using these methods and these variety's. I even had a Goliath to 6lbs.3oz but cracked.