2013 Trek Madone 4.7 rebuild advice

[Laloleg1]

Hi everybody, noob here. I just bought a used frame and I am about to start building my bike from scratch. I am looking for advice on what parts to buy. I have no experience riding except for stationary bikes. I am having issues deciding on what group set to buy; I know (I think?) the bike originally came with Shimano Ultegra 6800 but need some advise on weather I should buy all the hardware as a set or take advantage of the project and upgrade it. Any advice on what to upgrade it to, size, etc. Would be greatly appreciated.

Very excited about this new project!

 

[Ajax Bay]

https://www.ebay.co.uk/i/163471448198?chn=ps £675 with Ultegra (but no spec)
https://www.ebay.co.uk/i/183356665802? £700 with Ultegra
https://www.ebay.co.uk/i/223313535324 £800 ONO with Ultegra and some upgrades and really good wheels.

So if you're building this frameset up from new, it's worth taking care that you don't spend disproportionately more than a complete second hand (of course) bike would cost to buy, ready to ride. I think that you'll find buying an Ultegra groupset quite expensive.
"Any advice on what to upgrade it to, size, etc." The frame is not worth any better than Ultegra and frankly I'd put on 105. What do you mean by "advice on . . . size"?
The fun the OP gets out of a project like this is a very individual, personal thing: some cyclists would thoroughly enjoy sourcing the parts here and there; others would prefer to minimise hassle and buy a groupset. The OP's 'advice on size' request raises concern (for me) and maybe partly why noone else has responded.

 

[Grant Fondo]

Thats a great frame! I had a test ride on one at my LBS. Agree with Ajax advice. Would put 105 on it and the residual saving from Ultegra on best wheels you can get.
https://www.merlincycles.com/shimano-105-5800-11-speed-groupset-72462.html?source=PHG
Some good wheelset choices from Merlin as well.