Depending on the gun store most folks don't know squat about LR rifles. The M70 is a fine rifle, the 270 wsm is not as well suited for LR. The choice in high bc bullets is just not there.
You would be better served with a 300 wsm, 300 win (capable of higher grain bullit) , 7 rem (lower recoil) 300 wby (wow but expensive ammo). Going big 338 rum 300 rum 30-378 wby,
I would say a Savage ( same price range) would be a better choice, or a Weatherby mark V (3 times the price)
You can also stick with what you got and get very proficient with the 270 out to 600/700 or so and after a while rebarrel and rechamber. With the 270 wsm options will be limited due to the short action and bolt face.
Don't forget on your way to 1500 you have to be able to do 3,4,5,6,700 etc so all is not lost if you are "stuck" with the 270. Because it is a fine caliber just not directly for what you want.

I don't think your friends at the gun shop know what their talking about if they recommended the 270WSM for long range shooting.
Hengst has some good advice regarding rifles and cartridges. I would also recommend the Savage in one of their bench rest models but in a 6.5x284. It has the ballistics to match any 7mm or 30 cal out to 1500 yards, that is if your just shooting paper or targets. If games on the menu, then the others would work better as the heavier bullet with a high ballistic coefficient will deliver more energy down range than the 6.5.

I like the Win Mod 70 for average hunting conditions but I do not consider it a long range shooting tool. You need a more accurate barrel than the typical M70 offers. I like premium barrels on my long range rifles but there are some reasonably priced rifles out there. The Savage long range rifle is not a bad choice. The snipercentral.com Rem 700 entry package in .300 Win Mag for $1250 will be real hard to beat as a long range hunter. That rifle in .308 is a great paper puncher and the snipercentral Howa 1500 entry package would be even better for $1100. The .308 is not good for hunting beyond about 400 yards but it is a renowned paper puncher out to 1000 yards. I have a Rem 700 Sendero that shoots pretty well as a long range tool.

As far as cartridge, it is your choice but here are some thoughts: The .270 WSM will actually do quite well with 150g Bergers. The 7mm WSM is becoming a hot long distance winner. The .300 Win Mag carries enough energy for long range hunting out to 800 yards. There are good heavy long range, very low drag bullets in most calibers today (including .270) so I don't consider that to be a constraint anymore. See Bergerbullets.com or Sierra Match Kings among others. The bigger you go in cartridge size, the more recoil you will experience and that is a bad thing for long range accuracy. You can compensate for increased recoil with rifle weight, recoil pad and muzzle brake enough to make a .300 Win practical but you will have to work at it. That is one reason the 6.5x284 kicked tail... few of its owners had flinches and that remains a top cartridge for long range paper punchers. I use a .300 Dakota for 1000 yard hunting for game up to elk size and the .300 Win is pretty close to that. You should plan to pay as much for the scope as you do the rifle if you are serious about long range shooting.