my 1st gen i3 will bottleneck the r9 270 oc
Maybe, but it very much depends on resolution and graphics options. e.g. You could absolutely shift the bottleneck to the graphics card by running very high resolution & ultra graphics settings. Therefore, you should manually optimize your gaming experience by lowering your graphic options until you are bottlenecked by your CPU, and then adding back eye candy (higher settings, more AA, etc) up to the point where your graphics cards starts being the bottleneck. At which point you are making the most of both how
many frames your CPU can spit out, and how
pretty you GPU can make them. Some increased graphics options tax
both the CPU & GPU, so it isn't always quite this cut & dry.
will it be bad like reducing its lifespan because he can't work effectivly because of the bottleneck.
No.
the r9 270 will be as effective as a r7 260 because of the limitation the the i3 gives.
Not really; the 270 will allow you to turn up graphic options and/or render at a higher resolution while maintaining similar frame rates.
EDIT: Oh, you could consider holding on the 750ti; Nvidia has this thing called Geforce experience (iirc) which could (hopefully) do most of the graphics configuring for you.
Going by your post, it sounds like the kind of thing a user of your level might find useful.
EDIT2: It bears mentioning that AMD has a similar service running through the Raptr client, but after 'using' it for a few weeks now, I wouldn't dare suggest that a user rely solely on Raptr for configuring their games: too many unknown titles to be a viable comprehensive solution. Although, I have to say that
in the cases where Raptr did recommend optimal settings, they weren't half bad. I guess.