Wider rear tires were the rage for a while in the 1980's but tire technology has changed since then. With modern 185 tires I think you would introduce handling problems in tight cornering as the front tires break loose but the rears don't.
14" wheels are fine and allow a taller sidewall, which improves ride quality.
15" wheels will allow a shorter sidewall which will increase steering response and reduce tire flex. The downside will be a slightly harder ride. You will also have a better selection of tires in this size.
If you don't care about originality I would personally go with 15" wheels in a 6" width, combined with a 195/60R15 tire. This will be slightly taller overall than stock (increased rolling radius) so your speedometer may read a few percent slow unless you have it re-calibrated.
You can certainly save the money and just get some decent 14" tires. If you can find a good 195/65R14 then it would be a great compromise between ride and handling, but I was not able to find a good tire in this size here in the US.
Here is a list of wheels that will potentially fit an MGB, collected from numerous sources on the web. No guarantees that anything here will have the proper offset so check carefully before proceeding!
Acura Legend 86-91, CL, Vigor
Acura CL 2.3/3.0
Acura TL 2.5
Buick - Special '61-'63
Chevy II all 4-bolt
Chevy Corvair all 4 bolt
Chevy Nova ('61-'70)
Chevy Sprint '85-'87
Datsun/Nissan - most models to '89
Datsun roadster -early
Datsun 260Z, 280Z / ZX, turbo '70-'85
Datsun 240Z - needs chamfered nuts
Datsun 240SX (early) 89 - 94, 95 and up (4 cyl)
Dodge Colt, Plymouth Arrow RWD 79 - 92
Eagle Summit 86 - 92
Ford Falcon all 4-bolt
Ford Maverick all 4-bolt
Ford Granada all 4-bolt
Ford Capri 91 - 91
Ford Festiva
Ford Mustang all 65 - 68 all 4-bolt
Ford Mustang II
Geo Metro '88-'98
Honda Accord 90 up except V6 Accord
Honda Prelude '92-'96
Hyundai all
Infinity G20 91 - 94
Infinity M30 90 - 92
Mazda 323 86 - 89
Mazda 626 88 - 91
Mazda GLC 81 - 85
Mazda RX-7 GSL 84 - 85
Mazda RX-7 SE 86 - 88
Mitsubishi/Eagle
Mitsubishi Gallant 83 - 97
Mitsubishi Mirage 88 - 92
Mitsubishi Precis 87 - 94
Nissan/Datsun - most models to 89
Nissan 200SX 80 - 88
Nissan Altima, Stanza 93 - 98
Nissan 240Z, 260Z, 280Z /ZX, turbo 70 - 85
Nissan 510
Nissan B210
Nova ('61-'70)
Oldsmobile - F-85 61 - 63
Plymouth - Arrow 79 - 88
Plymouth - Sapporo 79 - 88
Plymouth-Mitsubishi Conquest (15")
SAAB - 900 79 to '87 come in 5.5 x 14, 5.5 x 15, or 6 x 15
SAAB - 9000 to '87 (not all?)
Sprint '85-'87
Suzuki Swift '89-'98
Toyota - most exc. MR2 and P.U. to '89
Triumph TR 1..5
Toyota Celica RWD
Toyota Corolla RWD
Toyota Supra 4 lug
Triumph TR 2-6
Volvo P1800 68 - 70