I'm going to disagree a little with the Clagster here:
Capelli stripes: firstly, I'm not sure that stripes are a priority for you at all with your style restrictions/preferences. The strong associations with private schools, sports clubs and military regiments are nto a problem unless yours has a meaning recognised by some gnarly old banker and not by you! But more generally, and especially as you will be wearing them with a solid navy or grey suit, they do smack of uniform. Not that you shouldn't ever wear a stripey tie, but with your requirements, I think it might be low on the list. And secondly, the first tie you picked is I think quite presentable.
ET: Clag is right about the shantung, but I think both grenadines are fine, and there's nothing wrong with purple as a conservative tie choice. It's lovely with a grey suit. I'll come back to grenadines, though.
Vanda: I don't have any Vanda ties (I should add "yet" as they look great and I love their ethos), but I think your first two here are a bit too soft and casual. The last one is OK, but there are better.
So, to actual recommendations:
If we're taking navy ties as read, then the colours I mentioned above are the priorities I think. And the consensus advice on neat small patterns as your default, is bang on. I'd go as far as to say that neats are all you need, actually in preference to solids at all, for the simple reason that you're so restricted in your choice of suit and shirt. There is very little texture or pattern in your professional wardrobe, and a good outfit needs some. All smooth and solid (and this is something I've improved on myself after seeing good examples on the forum over the last year or so), is dull and lifeless. As you're stuck with solid white or blue shirts, solid grey or blue suits, and a simple white square at most, the tie is all you have left.
Sure, a heavy grenadine has texture that works a bit like a pattern. But a neat is a good place to be. If you do want a solid or two, I'd skip past the fine grenadines though. The transparency makes them a little light and whimsical for CBD I think. A better choice of textured solid might be a heavy wool or cashmere herringbone: neat and smooth, not at all rustic, but with a weight and subtle pattern that had some character. There are some interesting linen ties around that can pull off a similar trick in the summer. Not that you couldn't get away with a grenadine, I just think there are better options for you right now - SF compliance aside.
Neat madders or similar are really versatile. The Panta suggestions are great - I wore the green one today (a coluur that no longer seems to be in stock). But they are quite earthy in tone, and if you want something more "city", then a Macclesfield might be more you. The burgundy one you chose from Vanda would be a solid choice - though Vanda also has this flowery one that I think is lovely. If you do like the madders, then Panta's rust and burgundy options are begging for your attention.
While we're in winter time, a wool tie like this from Exquisite Trimmings, or a herringbone like this from the same, would be good friends to you. And in the warmer months, perhaps you could even throw is something a little lighter and brighter, like this from Henry Carter. And if that's not quite C enough for your BD, then that might be the time for your grenadine, in a suitably muted colour. Don't wear a black one though. I know Sean Connery wore a black knit in the iGent's favourite movie reference, but it really isn't right for CBD and a completely black/grey/white outfit sucks all the colour out of you. Navy is OK. Rust, burgundy or green would be lovely.
That's all for now. If you're going to buy two ties today, I can't say anything more sensible than "get the rust and the burgundy madders from Panta".