I want to invest in new small Laptop for all my Chess , analysis, videos, PDF's etc.

What would chess friends recommend?

one question : budget (if any) ? 

Maximum about $1000 or £800

https://www.laptopmag.com/articles/sub-1000-gaming-laptops

https://www.cnet.com/topics/laptops/best-laptops/budget-laptops/

(anything that you wish with i3/i5 build in SSD  it will make you happy for coming 7 years )

Could you advise if a laptop with the following would be suitable to play and run a chess engine/programme such as Fritz 16 on?

Dell Inspiron 1545 bought in 2009

Windows Vista

Celeron Dual Core CPU

4GB RAM

DirectX 11

Mobile Intel 4 Series Express Chipset Family

I advice go with MacBook air 

SAMSUNG GALAXY TAB S5E 64GB

It is a tablet but it works all the way...there is even a 128GB

I presume you're looking for a machine that will give you maximum performance at a minimum time cost. In that case, any decent dual core processor will do. When analyzing a crucial move, you'll probably spend three minutes or so if you're using a dual core.

However, with that budget you can do better. And if it's mainly for chess, then you'll probably want one of those 2in1's (part tablet/part laptop). Though, if you ask me, those are rip offs, unless you're going for one of those Microsoft brands that will price you something hefty.

he hasnt been on for over a year

Dammit!

You guys ever wonder, with these old posts, if our replies go back in time. In that case, my recommendation for a dual core fits the year, don't you think? That way I'm not outdated, right?

Just to let you all know I broke the budget and I bought a Dell Inspiron at £1400 said to have best build quality.

I think it's very expensive and recently bought a Chromebook for my daughter for my son at £195 , suits him fine.  Amazing machine for shool work. Any one any experience of Chromebook for Chess ?

Amazing price on those Thinkpads. I think your right we're in the era of disposable  PC's now and poor build quality reflects that. New ones still very expensive

No one has mentioned a good graphics card (although gaming machines would have one).  Don't you need that to run Leela?  

This means that in order to run Leela in full strength you will need a GPU preferably one that supports CUDA.
Running it on GPU with non CUDA Lc0 binaries means you will get many times worse performance.
Even worse running it on a CPU like normal traditional engines run, means you will get many many times worse performance.
Neural net weights in order to run fast enough they need a GPU. On CPUs they are slow as turtles.

http://blog.lczero.org/2018/09/guide-setting-up-leela-on-chess-gui.html

Right its not a necessity, but if your spending money anyway, its something to consider in your machine specs.  

Yes that set up would work fine for normal engines like stockfish, just not LC0, which is fine depending on what you want.

Yeah I don't think at my level it matters much which engine I use.  And even at the highest level it is questionable if Leela will come up with anything better than stockfish.  But GMs have learned some new ideas from these neural network analyses so it makes sense that some people would like to have it play around with.

Well, I'm a broker. Not the one you're thinking of, it simply means I'm broke. Not that it has anything to do with this.

Do not get your kid a chromebook! This is the stuff that makes the likes of Cartman cry, "why don't you just..."

Buy your kid something around $500, and they can't come running to you for a new computer for at least another two to three years.

Buy your kid something around $1200, and they can't come running to you for a PlayStation either.

It's simple economics. John Nash himself would approve it.

wait he came back

And he's got himself a great build. Put some legs on that thing and we can call it a Reel Steal movie.