Well, to be honest, this list lacks in many areas. Just trying to help.
Apart from what Ailaros said.
0. What I'd drop in order to get points to take what I offer

would be:
dozer blades, basilisksx2, special weapons squad with meltas, Penals (unreliable, there are better alternatives). If it's an all comers list - maybe 1 hellhound too.
1. Anti-AV14 is seriously lacking, even if you have meltaguns. The problem is range. Meltaguns on feet on t3 guys with 5+ save ain't gonna live long enough to do anything. You need protection and/or mobility, and Chimera provides both. There's a reason why everybody and their aunt Mary runs Chimeltas nowdays, and it's not only because of
FOTM. Also, if you take 2 meltas, 2 more BS4 vets are going to waste their
BS with lasguns. I'd take 4 for
HQ.
Now if you don't want or don't have Chimeras, it's melta stormtroopers all the way. They can deepstrike, outflank, whatever, which gives you so needed mobility. Take them in squads of 5 with maxed meltaguns.
And one more rather good option is multimelta on hellhounds.
I myself in casual games run 2x vets with melta in chimeras and 1 hellhound with multimelta in 1.5k pts.
2. Long range anti-light-tank is lacking even more. Except for the Bassies which are extremely unreliable, you have no way to kill transports (i.e. Rhinos) on turn 1-2. Which means they are gonna get close and unload their content into your face. Close combat is not something Guardsmen likes...
3. Special weapons squad with Demo. Throwing demo suitcase is nice and cool, but it's 6''. Lack of mobility again. There are two ways to deliver the suitcase where it's needed, namely deepstrike (Marbo) and Valkyrie/Vendetta. Chimera is unreliable due to lack of speed for the task. Footslogging hardly works.
4. Basilisk. It's a shame that such a great model isn't that good. 36'' minimum range for indirect fire is huge. With direct fire, enemy can see you too, and we are talking about AV12 front in a list with not so many other
AV to shoot at. It will die. Simple autocannon or missile launcher can take it down from a range. They
can work, but they are extremely unreliable.
5.
PCS with a heavy flamer... it's better to take 4x regular flamers for that task.
6. Infantry squads with meltabombs... not sure if it works. You see no tank is gonna get close to them, opponent is just gonna shoot them down. The squads are not a threat from range so they'll likely get ignored. You will need to chase tanks yourself, which is not an easy task with footsloggers. And this leaves your bassies unprotected from deepstrikers, etc. It's better to give your squads long range weapons and deploy them around bassilisks (if you gonna keep bassies).
7. As for your original question, they are gonna survive long enough to shoot maybe once or twice and thats about it. The problem is in their
AV and the lack of more tanks in your army. Once basilisks are dealt with, all those numerous missile launchers, lances, etc. are gonna shoot at hellhounds, as simple as that.
8. Things you need: autocannons/lascannons for long range anti-tank (best: autocannons in infantry squads, vendettas with lascannons), meltas in chimeras/multimeltas for close range anti heavy tank, more long range firepower (
LR Battle tank, autocannons, bassies - already in your list but not the best choice, manticore, hydras...), close range anti-uber-infantry (plasma guns,
LR Demolisher), mobility & protection (chimeras, valkyries, vendettas). Guard is a shooting army, it must abuse every turn it's allowed to shoot, while your army apart from bassies can do something only when close n personal, which is a recipe for disaster. As a general rule of thumb, the more shots weapon has, the better it fits infantry squads (autocannon). The less shots and the better power - the more it fits for Veterans/Stormtroopers. This is due to BS3 vs BS4, you want to use everything to its fullest. The lower
BS the more shots you need to make it work. I.e.
CCS with 4x Plasmas will get 4-8x BS4 plasma shots, while 1 plasma in Infantry Squad will get 1-2x BS3 shot. 4 squads with 1 plasma each may not even get to shoot at the same target due to size and range. Which is more reliable?
9. Then again, actually playing and seeing is far better than listening to guys in forums

Maybe the list will work for you against your opponents. And if it won't, maybe you will see better what it lacks

Maybe I just failed to see your strategy plan or something. However if you are going yet to buy models based on this list, I really don't recommend it.