You can take the TOS Bundle to get the constitution bridge, some uniforms (not all, but the basic ones) and some stuff, como a shuttle and a phaser. Is a good starting point.
You can add later the Enterprise (400 c-points) and after some time, buy another ship, like a retrofit or better, just taking the blue phasers from enterprise to your new ship. You can keep the bridge from TOS Bundle in other ships easily, and keep any universal consoles and the phaser banks to your new ship.
But keeping the U.S.S Enterprise you have some problems, because the restriction of skills of yours bridge officers. You can buy other models of the same type of ship (like the movies) and keep all stuff you get in other ships in each new rank.
You can farm TOS ground weapons (phasers type 1, 2 and 3) and retrofit phaser banks for space from some missions. At VA they will be mk xi.
The only problem with your idea is that the TOS Constitution isn't going to work. There is however, a T5 Excelsior you can use (1600 CP) and if you add the retrofit phasers and the original connie bridge, it will be very 23rd century retro.
Flexiflo - I went all TOS including the old uniforms, old weapons, flew a constitution class... etc. I found that if you're smart about your tactics you can continue using the original constitution class all through the Lieutenant Commander rank & into the early Commander levels as well, and use the movie era constitution all through Commander but somewhere in the early Captain levels it's just not possible to remain effective in combat even with the tier 2 (i.e. movie era) ship.
Those old boats will take you far but there is a reason why the Federation comes out with bigger better vessels every few years. You can't really take those ships into end game stuff... however I still wear my TOS uniform proudly and pack old blue phasers on my admiral rank cruiser.
You can do everything except the Constitution and be okay for endgame. There is a mission "Everything Old Is New" where you can quickly repeat it (takes like 15 minutes) and get level-appropriate retro phaser banks, so when you're at Vice Admiral they'll be Mk XI and as good as any regular end-game weapon. The mission "Night Of The Comet" rewards retro phaser pistols and phaser rifles for arming your bridge officers, again level appropriate. So you can get up to Level 50, then run those missions a half dozen times each, and be ready to go.
For your ship though, the original Constitution just can't cut it beyond level 20. Some people might like to fly it anyways, but you'll have only a fraction of the firepower, equipment, and powers the end-game expects you to have. However, as mentioned above, the Excelsior Retrofit (the 1600-point one, not the 800-point version) is quite retro styled and is a match for any endgame cruiser, Odyssey included. Plus if you buy it when you hit 40, you can switch to it immediately and save your relevant ship token for if you ever someday decide to try out an escort or science ship besides.
Naturally I'll be holding onto the ToS for as long as possible, it might last abit longer seeing as my brother and I are going around together, him in an NX class flying yellow decoration. ("In a mirror darkly" eat your heart out.)
So we'll see how long we can last, but I will probably take the refit excelsior if things get a bit out of hand... have to admit, it's a shame the ToS Connie can't hack it through to end game, sure I never expected it to do fleet actions or PvP but doing the missions would have been nice.
I'm hoping that us going around in a pair will help us correct the lack of weapons a little bit, maybe help us last longer.
These characters are just for abit of nostalga, I've got a Commander Federation and a high ranking General Klingon character for serious play so... you know, why not Kirk it?
Some people have leveled to Vice Admiral with Constitution Class ships or Shuttles. It may be a little much for a newbie, since there are some things you first need to learn about managing your ship. But you could probably do most missions.
What you can't do is
2) Fleet Actions (it would at least be a very frustrating experience)
And you probably should not bother with Advanced or Elite difficulty.
For ground combat, I believe you can use TOS gear as long as you want, either some of it is levelling, or you can replay a mission at a higher level to get a level appropriate variant.
Before the update a person hit max level as an ensign in the ToS connie.
Toward the end she required a friend or so, but a trick as you level up is have a friend, and level match to that person. If he's a captain and you are a captain, your ToS connie will get captain appropriate hull. (as I remember)