Hello avvy,
Your itinerary seems logic, so basically we can't comment on the plan itself, but can just recommend how to handle rail part of it. Let's go step by step:
Madrid to Barcelona: since there are 4 people traveling easy option might be just to get so-called "Mesa" tickets (more about it on our Spain page -
http://europetrainsguide.com/Countries/Spain/Spain-RENFE.html), they are relatively easy to catch type of tickets and give a good value at the end. Otherwise you can also look into "Promo" tickets, which are up to 70% discounted, although a bit harder to catch, so if you decide to "hunt" for Promo ticket, then better to do it early. And finally, if you totally against purchasing tickets in advance (which is kind of required with Promo or Mesa tickets), but still have no desire to pay full fare (which is like 100+ euro per passenger with high-speed trains), then it's possible to use slower regional train or overnight Estrella train, both are cheaper options (although taking much longer)
Rome to Florence: two options here: a) purchase in advance (trenitalia.com) discounted "Super Economy" tickets for high-speed trains (start from only 9 euro per person) or b) don't bother with any ticket purchase in advance, but simply use a bit slower & much cheaper direct regional trains (full standard fare is just 20,25 euro)
Florence to Venice: same options as above - either Super Economy discounted tickets or regional trains. The only difference is that on connection from Florence to Venice there is no direct regional trains, so you'll have to make a change
Venice to Munich: here you have a choice of either direct train (daytime EuroCity or overnight train) or traveling during the day with change in Verona. For direct trains you can get discounted tickets on the same trenitalia website for as low as 29 euro (seats), 49 euro (couchettes) or 69 euro (sleepers). However again in order to catch the best price, you'll have to purchase tickets in advance.
Munich to Lucerne: as in previous cases here it is also possible to rely on discounted tickets, which can be purchased via bahn.de website (start from 39 euro). At the same time also possible to take a different approach and use the fact that there is 4 people traveling. German Railways (DB) offer special group passes (up to 5 passenger), in this case we speak about such pass in Bavaria region - Bavaria Lander Ticket. It will allow all 4 to travel from Munich to Bodensee lake (let's say Lindau) for just 34 euro, while then you can just take a nice ferry over the lake to Switzerland (Rorschach) and continue by Swiss trains to Lucerne (for Swiss part can be used bargain
SuperSaver tickets)
Lucerne to Zurich: above mentioned SuperSaver tickets is a good choice here, although even full fare tickets here aren't extremely expensive
Zurich to Paris: best and cheapest option here is to go with discounted tickets for high-speed daytime trains, they start from only 25 euro and can be purchased either via tgv-europe.com (we have a step by step guide on how to do it -
http://europetrainsguide.com/Advice/How-to-Buy-Train-Tickets/France-SNCF.html ) or Swiss Railways website ticket shop - sbb.ch/en/ticketshop (section "Lowest fares for direct services to major cities in Europe")
If you decide to stop in Salzburg, then nothing essential changes, just instead of discounted Venice to Munich ticket purchase discounted Venice to Salzburg one via same trenitalia website. While for Salzburg to Munich journey works mentioned above Bavaria group ticket (34 euro for 4 passengers)
p.s. it's kind of a lot of info above, so we usually suggest fellow travelers just gradually take a look at each option, check it out yourself on rail companies websites, think about what might be your choice etc., then if you have additional questions or concerns - we are always here & happy to help
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