
1. 3 layer soundproof on doors. Outer door skin, rear of inner door panel, rear of door card. I used DoDo mat, but of course there are many others to choose from.
2. Upgrade to Kevlar Meridian Signature speakers for the 100mm mid and 200mm woofer in door. Tweeter only if you are keen on sharp vocals or the classics. Having carried out 1+ 2, move the staging forward to reduce the input from the stock rear speakers, as they will distract from the tighter audio being delivered from the doors. I'm not familiar with the DSP settings of the 'Meridian Surround' 770W system, but if you generally listen to your music in 'surround' mode rather than Dolby Stereo, I'd say go ahead and fit the Kevlar upgrade centre speaker. On it's own, it's not going to make that much of a difference as it's only a 100mm mid with co-axial tweeter.
The Meridian Signature speakers come up on Ebay every now and then, although the 200mm woofers not so often. Alternatively the Kevlar upgrade speakers can be purchased new for reasonable price from the likes of Britcar.
3. If you want to have better quality input from the rears, you can keep the standard amp and go for the Audison and Bold combination using second hand speaker frames (or gut your own frames if you decide there's no going back). You'll have to do some soldering to match up the twin coil input for the Bold to the Jaguar connections and use some adapter rings to fit the new speakers into the frames, but apart from that it's plug and play as the speaker resistances will match what the Jaguar amplifier is expecting at the end of the wire. I could only source the Bold from Germany as it's not available for sale in UK.
Next level up from 1 - 3 would be full audio overhaul. Signal processor to capture OEM head unit output, new amplifier(s), speakers, custom cabinet, boot mounted sub, basically whatever your budget will stretch to. For me 1 - 3 produced a definite improvement, certainly on par with the Harmon Kardon in my Beemer and was an enjoyable exercise that I could undertake without needing much in the way of car audio knowledge. The F-Type is never going to be the best environment for listening to music, but for a reasonable sum and a little effort, it can certainly be improved.