2 top ASX shares I'd buy with $2,000 for October and beyond

I believe that some ASX shares would make great buys right now with $2,000 for October and the long-term.

The US election could throw up a lot of volatility over the next month (or four). Sometimes we have to ignore potential short-term problems and go with investments that seem like quality long-term ideas.

If I were buying two growth shares for the long-term, I'd go with these picks:

Pushpay Holdings Ltd (ASX: PPH)

I think the market is underestimating how much growth Pushpay can generate over the next year or two.

Don't get me wrong, the electronic donation business has been doing very well. The Pushpay share price has actually risen by 141% over the past six months.

I think there's more to come from the ASX share. It was able to beat its previous guidance for FY20 and I believe that it could beat its guidance in FY21. Pushpay is aiming to at least double its earnings before interest, tax, depreciation, amortisation and foreign currency (EBITDAF) to at least US$50 million in FY21. The unfortunate COVID-19 circumstances are boosting adoption of Pushpay's services. It also offers livestreaming capabilities for congregations. 

Part of the reason why I think Pushpay could do so well is because of its scalability. In FY20 alone it grew its EBITDAF margin from 17% to 22%. That came from just adding another US$30 million-ish revenue to its top line. In FY20 it made US$130 million revenue, it seems the business can become much more profitable as it steadily grows to its US$1 billion revenue target from large and medium US churches.

Over the longer-term, the ASX share could expand its technology to other religions in the US, other geographical markets or other not-for-profit sectors.

At the current Pushpay share price it's priced at around 38x FY21's estimated earnings.

A2 Milk Company Ltd (ASX: A2M)

The A2 Milk share price has been crunched almost 30% lower over the past two months.

Over the short-term, businesses will suffer some difficulties. A2 Milk seems to be going through some COVID-19-related pain right now.

For the second year in a row, A2 Milk's share price has suffered through August and September.  

I think the market is overestimating how much A2 Milk's earnings are going to be hurt over the long-term.

I believe this is a long-term opportunity to buy shares of one of the best ASX shares. The company is impressively growing its market share domestically and overseas, particularly in the US and China.

Daigou channel sales aren't the only way to sell to Chinese consumers. A2 Milk is seeing fast growth of its China business.

For the full 2021 financial year it's expecting revenue to be between NZ$1.8 billion to NZ$1.9 billion. That would represent growth of between 4% to 10%, up from NZ$1.73 billion in FY20, with a fairly similar earnings before interest, tax, depreciation and amortisation (EBITDA) margin.

The company continues to add thousands more stores to its distribution network across China as well as the US.

I'm particularly excited by the expansion into Canada with its agreement with Agrifoods. The more countries that A2 Milk can sell its products into the better. It increases A2 Milk's total addressable market and gives it a longer growth runway.

In the short-term, Melbourne's lockdowns seem on track to be lifted soon which should help boost sales.

In my opinion, the ASX share has many years of good growth ahead. I view this selloff as a very attractive buying opportunity. I don't know what A2 Milk shares will do over the next few weeks, but I think it can do well over the coming years.

At the current A2 Milk share price it's trading at 21x FY23's estimated earnings.