two problems you will run into and some of my experiences with tandem trailers and tires:
first, smaller tires, in general, can carry less max weight. with two 3500 lb axles, you are building a 7,000 lb trailer. that means you need each tire to carry a minimum of 1750 lbs. you should also have a decent safety margin (you will need it!). on my 15" diameter tires on my 20', 7000 lb trailer, each tire in the load C range can only carry a hair over 1800 lbs. these tires cost about 85 dollars to replace mounted and balanced. i know this because i replace several a year due to overloading and due to the crappy nature of the el cheapo tires that came with the trailer when new. to go up to a load d or e, now you are talking 110 to 150 each mounted and balanced. that is 600 for four new tires! plus, a spare. also keep in mind on a tandem trailer, it is recommended to replace both tires on a side if you have a blowout when loaded because the good tire on that side bears all the load when the second tire blows out and it damages the seemingly good tire internally when you overload it by twice its recommended capacity. best to avoid blowouts by sizing the tires with a good safety margin.
second, you do not want an odd size trailer tire you have to order. you want a commonly available tire and a spare because you will get flats. on a tandem trailer it is very easy to go from a low tire to a ruined tire because you won't notice it right away when going down the hiway. you want to be able to pick up a new tire at any decent size town you happen to be close to. you don't want to have to park you nice trailer in the median in these hard economic times. it's just too tempting a prize for someone in a desperate situation. start with a common size tire rated for trailers and carry a spare.
hope that helps! i run 175/75-15ST in load range C. i have found locally that mastertrac tires last the longest in this load range.
as far as clearance and COG, low is good but it depends on how long the trailer is. longer requires higher clearance so the tail will clear when going over uneven ground. with larger tires, you can probably just go with higher fenders to get whatever clearance you need.
i'll also mention that probably the most critical design decision you face is the location of the axles on the frame. farther back tows more smoothly and less chance of fishtailing, but requires the tow vehicle to carry more tongue weight. make sure you understand the tongue weight relationship and the real world ability of your tow vehicle to be comfortable when towing with whatever weight you decide to put on the ball. sometimes this is the same as the manufacturer's specs and sometimes not.
one last thing about fabbing a tandem. professional builders have a good feel for how strong their steel is and how much reinforcement to add. a hobby builder or first time builder will be tempted to over do this which adds a lot of weight to the trailer. take a look at some designs you like before you start. my trailer weighs about 2200 lbs empty. that eats quite a bit of the 7k load capacity. don't ruin your hauling capacity by overbuilding the trailer and adding too much weight.
so, there it is! pick a common tire size in your area. pick tires large enough to carry the weight plus safety margin in the load range you want to pay for. locate axles accordingly. and yes, i would put brakes on one axle.amp
