I did it with British ones due to the fact that they were the easiest to aquire at the time of the break up. For self defence RAM and ESSM will do but for longer range I prefer ASTER purely for the fact more nations closer to home use it. Largs Bay is in the process of being aquired for 100,000 due to the fact that Wales can stop Birmingham's water so quickly the English will give us almost anything we want.
Also with regards to the Spruance there is the process of acquiring a Cavor based Cat and Trap carrier to operate Sea Gripen, Merlin, E-2 and F-35C
If you are wondering how there is a huge budget it is because England is billed for lots of little things (including Elan Valley water) and me being a Welshmen whom fells quite at home with defence spending fell this is the best thing to do.
Also the City Class was aquired cheap as the radars were there test BAe ones and the Sea Wolf was taken off the Type 22
I've never been a fan of Sea wolf, and ESSM seems like a much better missile, though I can understand using it, if you are able to get a bunch of them cheap, or nearly for nothing. Still, not a great longterm solution, though. If you are going the Aster route, then you might think of using some version of FREMM as your frigate. They aren't badly priced, and offer reasonable capability, and commonality with several NATO nations, at least regards systems, though the British did some odd monkeying around with their version of Aster, from what I recall. (I could be wrong of course)
Sounds like this is reasonably well thought out. Cavour is my choice my own AU; there really isn't much not to love about it on the whole, and it can be upsized & upgraded. Likewise, Sea Gripen is likely an effective system that meets your likely threat level at a decent price--l expect cheaper than navalized Typhoon, though I'd really have to see a detailed price comparison between the two to know for certain. In light of the huge cost, you might consider doing away with F-35. I can't even justify it for Pallamara, which has a larger budget than the UK. (76 vs 69.3 Billion) Other nations have already backed out of the programme as well, and I take that as a strong hint. Unfortunately, there aren't many other options available for now, but the price will (hopefully) come down at some point.
I'd be interested in hearing about the setup for your airforce. Tornado ADV (F-3?) seems like a decent idea in the short term, and the RAF is trying to get rid of it. You could likewise go for the F-15S, which can do about anything you'd need-- expensive, though I can't imagine anything nearly as bad as F-35. Stick a few of these in the Falklands, and Argentina won't even dream about going near the place. The threat over your own territory is almost nonexistant, but you could do worse than to bring a couple of Squadrons of Silent Eagles to the NATO table. 50 of them gives you 15 for the Falklands, two squadrons for home or NATO, and a few spares. Given the multirole nature of the aircraft, it can replace a lot of other types of stuff in the inventory. A (very) slightly less capable aircraft is Superbug, and I'd go with the two seater F version of that.
Another area of interest is what political relations with Eire are like, given both the Celtic nature of the commonwealth, and the inclusion of Northern Ireland?