My opinion, tear down the engine first; then order parts. That way, you will know better which parts you need, and which sizes you need (for example, whether the crankshaft journals have previously been ground undersize or need to be ground undersize now). You'll also be less tempted to reinstall marginal parts.
With a lot of blowby, you may need to have the cylinder bores machined oversize and install oversize pistons and rings; or possibly just replace the pistons you have with the same size (which may already be oversize). Whether they get bored or not, plan on honing afterwards to get a good cross hatch pattern.
Inspect the valve seats and guides. Unless they are absolutely perfect, you'll probably want to machine the seats and replace the guides. Maybe the valves too. If the engine is 'tired', chances are that it needs new valve springs (but you can check seat pressure to find out).
Inspect rockers & rocker shaft. With lots of miles, probably the rockers will need to be rebushed and refaced; the shaft replaced.
There is lots more (eg timing chain and sprockets); get the factory manual and follow it. Check everything!
PS, or there is the approach I seem to wind up following more often : just stuff some new rings and bearings in it and throw it back together. Plan on tearing it down again in 20-30 thousand miles to do it "right". I've been putting off a proper rebuild for almost 30 years now (and two different TRs) ... :laugh: