If you want a sporty luxury car as an investment, the way to go is Back To The Past! A Cougar from 1967-69 was a car that could be ordered up as sports/luxury in the XR7 package and if you REALLY wanted to do some serious gas pedal pushing, you added the GT package to get the 390 V-8. Cougs are undervalued compared to the other muscle/pony cars from that era and nice ones can be had for less than $10K.
If you go GM, then the Pontiac Grand Prix in 1969-70 offered a good range of packages from the 400 V-8 with AT/PS/PB to a 428 (1969)/455 (1970) that romped and stomped. Plenty of GP's came with tilt wheel, A/C, power windows, vinyl roofs, factory rally wheels and the usual AT/PS/PB. This is usually considered the best sports/luxury car GM made that gave fine emphasis to both the performance and comfort factors. Nice examples go for $10K or less.
MoPar's performance/luxury offering was the 300 letter series through 1965 and the Hurst 300 made in 1970. You got the options list generally associated with the New Yorker and the 440 Magnum that powered up so many cop cars as well as muscle cars back in the day with the 1970 300 Hurst as well as a spiffy body trim package. The 1959-65 300 letter series were powered by the 413 V-8. MoPar only accounted for 10% of the market back then and that means finding MoPar goodness is a lot harder than doing so for GM/Ford products. The resullt will be higher prices due to the relative scarcity and this shows up in MoPar muscle cars from that era like the Charger, Challenger and Barracuda, where even a junk body will be close to $10K. The 300's command quite a healthy price when in tip-top shape, so you likely won't be able to afford one from 1963 on back but the 1964-65 and 1970 model prices have not really taken off into the stratosphere yet. Keep your eyes open and one of these may be available.
When you buy an older car you create the chance for an increase in value by how well you restore it or how well you maintain what you get. I'd avoid the real museum pieces that have uberlow miles since their value is all wrapped up in the mileage. Find one that is good to go and able to be a daily driver. Keep it a couple years, watch the trends on Barrett-Jackson to see if the car goes hot in the market, then sell it for a profit. At worst you wind up using the car and giving up a percentage of value that will be in proportion to how much you used it up. If the use was light and a few paint chips happened while everything stayed solid and clean, then you'll get as much as you paid for it if you paid the right price. Research price/condition matches to know what "right" is.
Now if you are willing to say "it's not an investment, it's an expense", go get the Charger. Chrysler is sitting on a 120 day inventory supply and the market is quite depressed for these cars both for new and used models. You may also wish to consider a Magnum, the modern-day equivalent of a 55-57 Chevy Nomad in that it is a sporty wagon. If you buy new you get a lifetime powertrain warranty. If you go used, a Charger with a V-6 should be able to be had for around $15K. The SRT-8 is a high priced performance package so don't expect to find too many out there and when you do, you'll pay a hefty premium to get it. Going new with an SRT-8 means paying in the $30K's.
The Bimmer depreciates like crazy and is expensive to fix. Look around in the 1990's for top of the line BMW's under $10K if you are enamored of Euro luxury/performance. Back then they could run up in the high 5-figure territory for a V-12 750IL and today you can have that car for about 15% of it's original sticker. Make sure you have a shop in BR that you'd be happy with as you will have some Big Bills to pay.
Mustangs are NOT luxury performance. The T-bird from this decade has the luxury but not the performance. About as close as FoMoCo came to matching the two qualities lately was the Lincoln Mark VIII from the 1990's with the high performance 4.6 that I believe was rated at 285 HP and the Mercury Marauder from 2002-03 with a 4.6 with an output in that area. The Mark can be had for $5K or less in great shape while the Marauder will run in the $20K's for one in tip-top shape/low miles. The Marauder, if it follows the trend of the 1990's Chevy Impala SS, will stay at the current price points so long as you don't "use it up" so you'd have to decide how much use you want to give a really nice one. I'd expect a 3 year period of running up 40K on the odometer but keeping the cosmetics up on a low mileage Marauder would leave you looking at a sale price of $15K. If you hardly drove it, the value should stay close to what you paid for it.
If you want to get off as cheaply as possible and wish to emphasize performance, then the Mustangs are the way to go. They do come with A/C, PW, PDL, tilt, cruise, buckets and console but no one ever considers them as a luxury sporty car.
An intriguing way to go is to find an older Jag with a smallblock Chevy transplant for under $10K. Make sure you aren't very tall and are skinny though as interior space is limited. However you will have the best interior trim of all in regards to the leather and wood. The amount of depreciation on one of these will be in line with how much you use it up. Make sure it's a good install on the engine instead of some shadetree job and check the electricals well as Jags are notorious for having a poor electrical system.
Financing: There are plenty of options but since you are in the military, the best one is to go see your credit union first. They know you will be paying via an allotment if things are like they were when I was in. The lowest APR's offered by the manufacturers are for customers with top notch credit scores. The credit union will offer a better rate than the high-risk credit-extending companies out there and you will get a chance to build your score rather nicely as car loans count for a higher score than your basic unsecured credit card. You will still want to get a couple of those to flesh out your credit profile, so also check with your credit union for their credit card offers.
Now it's up to you to decide whether to buy and figure the vehicle is an expense, buy and know how to keep one going as an investment, go import for cachet but be willing to bite the bullet on maintenance or go domestic to hold that expense down and whether you should slant more towards the performance or the luxury side. There are plenty of options to pick from and plenty of cars to buy, so don't rush your decision to buy and once you know what you want, wait patiently for a good deal. Times are tough and it's a buyer's market.
Rick