SaaS or subscription services are generally consider digital goods for tax purposes and are subject to US income tax and depending on the state you register in state level income and sales tax also.
First forming a US corporation will require filing a US corporate tax return and paying US federal income tax on the net profits of the business. Being a non-resident owner does offer some planning opportunity by selecting a state that has no state level income tax and minimal or no sales tax. I would suggest that Wyoming may be a good choice for you. You also have the ability with a corporation to pay a reasonable fee back to the non-resident owner and affiliated entities for services provided to the US entity. I would caution you that any such transactions with foreign related parties are required to be disclosed on the corporation's tax return and are subject to rules on Transfer pricing of tangible goods between controlled businesses
An LLC has many of the same tax considerations as a corporation regarding sales tax with the major difference being in the US federal tax level. A single member LLC is by default a disregarded entity for US federal tax purposes which is just a fancy way of saying that for taxation the US looks to the LLC as simply an extension of the non-resident owner. That will mean the non-resident owner has to file a US non-resident tax return to report profits from any US sourced income, which as already mentioned typically includes digital goods, with certain exceptions which may apply in your situation because you are in India.
The US and India have a tax treaty that says your business profits are only taxed in India, unless you conduct your business through a permanent establishment in the US.
Sorry this is a long but highly relevant definition from the treaty about what is a permanent establishment:
1. For the purposes of this Convention, the term “permanent establishment” means a fixed place of business through which the business of an enterprise is wholly or partly carried on.
2. The term “permanent establishment” includes especially:
(a) a place of management;
(b) a branch;
(c) an office;
(d) a factory;
(e) a workshop;
(f) a mine, an oil or gas well, a quarry, or any other place of extraction of natural resources;
(g) a warehouse, in relation to a person providing storage facilities for others;
(h) a farm, plantation or other place where agriculture, forestry, plantation or related activities are carried on;
(i) a store or premises used as a sales outlet;
(j) an installation or structure used for the exploration or exploitation of natural resources, but only if so used for a period of more than 120 days in any twelve month period;
(k) a building site or construction, installation or assembly project or supervisory activities in connection therewith, where such site, project or activities (together with other such sites, projects or activities, if any) continue for a period of more than 120 days in any twelve month period; (l) the furnishing of services, other than included services as defined in Article 12 (Royalties and Fees for Included Services), within a Contracting State by an enterprise through employees or other personnel, but only if: (i) activities of that nature continue within that State for a period or periods aggregating more than 90 days within any twelve month period; or (ii) the services are performed within that State for a related enterprise (within the meaning of paragraph 1 of Article 9 (Associated Enterprises)).
3. The term “permanent establishment” shall be deemed not to include any one or more of the following:
(a) the use of facilities solely for the purpose of storage, display, or occasional delivery of goods or merchandise belonging to the enterprise;
(b) the maintenance of a stock of goods or merchandise belonging to the enterprise solely for the purpose of storage, display, or occasional delivery;
(c) the maintenance of a stock of goods or merchandise belonging to the enterprise solely for the purpose of processing by another enterprise;
(d) the maintenance of a fixed place of business solely for the purpose of purchasing goods or merchandise, or of collecting information, for the enterprise;
(e) the maintenance of a fixed place of business solely for the purpose of advertising, for the supply of information, for scientific research or for other activities which have a preparatory or auxiliary character, for the enterprise.
4. Where a person – other than an agent of an independent status to whom paragraph 5 applies – is acting in a Contracting State on behalf of an enterprise of the other Contracting State, that enterprise shall be deemed to have a permanent establishment in the first-mentioned State if: (a) he has an habitually exercises in the first-mentioned State an authority to conclude contracts on behalf of the enterprise, unless his activities are limited to those mentioned in paragraph 3 which, if exercised through a fixed place of business, would not make that fixed place of business a permanent establishment under the provisions of that paragraph; (b) he has no such authority but habitually maintains in the first-mentioned State a stock of goods or merchandise from which he regularly delivers goods or merchandise on behalf of the enterprise, and some additional activities conducted in that State on behalf of the enterprise have contributed to the sale of the goods or merchandise; or (c) he habitually secures orders in the first-mentioned State, wholly or almost wholly for the enterprise.
5. An enterprise of a Contracting State shall not be deemed to have a permanent establishment in the other Contracting State merely because it carries on business in that other State through a broker, general commission agent, or any other agent of an independent status, provided that such persons are acting in the ordinary course of their business. However, when the activities of such an agent are devoted wholly or almost wholly on behalf of that enterprise and the transactions between the agent and the enterprise are not made under arm's-length conditions, he shall not be considered an agent of independent status within the meaning of this paragraph.
So, if you can avoid the above criteria and not conduct business through a permanent establishment in the US, then you will most likely want to choose to be a single member LLC for federal tax purposes and avoid US federal income tax. You would still be subject to state franchise taxes and sales taxes which as I mentioned you can often plan around by choosing the right state in which to incorporate. Also your income would still be taxable in India, if it is not taxable in the US.
Finally US non-resident taxation is a fairly complex and very fact based area of US tax law, so it is probably worth your having a conversation with a US tax professional to consider all the specific "facts" about your business to be sure you structure the operation to minimize your tax liability. Simply changing one fact can often change the answer as to where you will be required to file and pay taxes.