What's the best laptop brand out of HP, Lenovo, and Acer?

I'd say hp but it's a personal preference

HP--I repair my neighbors' HP laptops regularly. Mostly hard disk failures.
Lenovo-- My G555 laptop has had 3 video chip detachments. Heating problem is common. Now I will try another motherboard in it.
Acer-- My Aspire 5610 Core Duo with Vista is over 6 years old and works fine. Not sure about current ones.
Dell-- My R 15 Inspiron with i3 Intel and upgraded to Win 8.1 is 19 months old and runs well. Has touchscreen too, was on sale (a 2012 model left over).

HP, hands down. Although, If you were choosing from any brand, I'd get your hands on an Asus.

Old data, or new data?
First of all, price is a better judge of reliability than brand.
G series Lenovo, Inspiron by Dell, Pavilion by HP, and cheap Asus or Acer, are all low reliability.
Of major brands, Asus and MSI are design and manufacture, and Lenovo Thinkpad is a co-design and manufacturing. A Lenovo is only a Lenovo (other than Thinkpad) by it's label and customer service. 80% of HP is now subcontracted. This has been increasing for years, and now, HP is pulling an Acer move by trying to sell as much cheap junk as possible. All of Acer laptops is contracted out since they split off their Wistron as an independent company. Now, they are fine procurement groups choosing what is offered by the manufacturers.
This is now a few years old, but describes it:
http://www.xoticpc.com/laptop-manufacturers-really-makes-laptops-ip-11.html

Now, Dell, which had the best customer service in the industry, changed back in 2007.

The latest available actual tracking report:
http://www.rescuecom.com/...15-q1.aspx
has HP on bottom, and Acer moved up. Lenovo has improved, mostly by minimizing the G series as a set of their business, where HP became the leader of cheap laptops.

It is more price related than brand. Lenovo is the best of the bunch if not the G series.
Acer is a random issue by model since no two models are the same. They shift around among a few true manufacturers, but since they exited the focus on cheap volume, they improved.
I don't trust HP any more.
Battery life is usually a lie for all of them.
Look closely for ethernet as a technical feature and for bluetooth.
Ethernet is either 10/100 fast or 10/100/1000 gigabit. It is only used when cable connected to internet for fastest downloading and streaming and few people look for one or the other. It costs $0.60 extra to use gigabit ethernet in the design. If they use that, they cheaped out on everything using the cheapest parts overall.
With bluetooth is less than $1 on the wireless. It is another place to sneak out cost.
The brands you show do not make the laptops, and instead they are choosing design features.
A high failure rate is the dc-in connector. Many Lenovo models use a re-designed better input power.
Attached battery or accessible battery pack by latches or 2 screws is better than encased batteries. Models with a wide range of graphics card and cpu options are more likely to overheat than ones offering few choices.

Very old mid-priced from 2011 and earlier were mostly well-made. Lenovo G555 was a trash product of 2010 cheap and showed it over time.

So, it is more models and cost than brand, but on average now, Lenovo is 1, Acer is 2, and HP is 3 on average.
Anything under US$400 is questionable reliability.
check performance benchmarks here:
https://www.cpubenchmark.net/...u_list.php

Of the three brands you mention, I'd lean towards the HP brand. I've had my HP for a couple of years now with no problems what-so-ever.