Under the section ‘Beliefs’ this article explains how Pentecostals view having an experience of God comes through baptism with the Holy Spirit. Part of the article says this:
Baptism with the Holy Spirit: This is an experience distinct from baptism into the body of Christ. In this baptism, Christ is the agent and the Holy Spirit is the medium... The majority of Pentecostals believe that at the moment a person is born again, the new believer has the presence (indwelling) of the Holy Spirit. While the Spirit dwells in every Christian, Pentecostals believe that all Christians should seek to be filled with him. The Spirit's "filling", "falling upon", "coming upon", or being "poured out upon" believers is called the baptism with the Holy Spirit. Pentecostals define it as a definite experience occurring after salvation whereby the Holy Spirit comes upon the believer to anoint and empower them for special service
The main purpose of the experience is to grant power for Christian service. Other purposes include power for spiritual warfare (the Christian struggles against spiritual enemies and thus requires spiritual power), power for overflow (the believer's experience of the presence and power of God in their life flows out into the lives of others), and power for ability (to follow divine direction, to face persecution, to exercise spiritual gifts for the edification of the church, etc.).
The above article says speaking in tongues (or experiencing any of the other gifts of the Spirit) are evidence of having received Spirit baptism. Such an experience can also be manifested with an outpouring of joy and praise, and a desire to serve God wholeheartedly. As the article says, they believe this baptism with the Holy Spirit “empowers them for special service”. While there is only one baptism with the Spirit, they say there should be many infillings with the Spirit during the life of the believer.
Since the majority of Pentecostal denominations believe in the doctrine of the Trinity, then to experience the gifting of, or the indwelling of, the Holy Spirit is to experience God.
Your secondary question asks if any “particular types of divine experiences accepted by Pentecostal/Charismatic churches that other denominations would be more reluctant to accept or actively promote?” In the main Wikipedia article above, I found a section that draws distinctions between Pentecostal Trinitarianism and Oneness Pentecostalism
During the 1910s, the Finished Work Pentecostal movement split over the nature of the Godhead into two camps – Trinitarian and Oneness. The Oneness doctrine viewed the doctrine of the Trinity as polytheistic.
The majority of Pentecostal denominations believe in the doctrine of the Trinity, which is considered by them to be Christian orthodoxy; these include Holiness Pentecostals and Finished Work Pentecostals. Oneness Pentecostals are nontrinitarian Christians, believing in the Oneness theology about God.
In Oneness theology, the Godhead is not three persons united by one substance, but one God who reveals himself in three different modes. Thus, God relates himself to humanity as our Father within creation, he manifests himself in human form as the Son by virtue of his incarnation as Jesus Christ (1 Timothy 3:16), and he is the Holy Spirit (John 4:24) by way of his activity in the life of the believer. Oneness Pentecostals believe that Jesus is the name of God and therefore baptize in the name of Jesus Christ as performed by the apostles (Acts 2:38), fulfilling the instructions left by Jesus Christ in the Great Commission (Matthew 28:19), they believe that Jesus is the only name given to mankind by which we must be saved (Acts 4:12).
The Oneness doctrine may be considered a form of Modalism, an ancient teaching considered heresy by the Roman Catholic Church and other trinitarian denominations. In contrast, Trinitarian Pentecostals hold to the doctrine of the Trinity, that is, the Godhead is not seen as simply three modes or titles of God manifest at different points in history, but is constituted of three completely distinct persons who are co-eternal with each other and united as one substance. The Son is from all eternity who became incarnate as Jesus, and likewise the Holy Spirit is from all eternity, and both are with the eternal Father from all eternity.
The Protestant view of speaking in tongues is that while every born-again believer has the indwelling of the Holy Spirit (1 Corinthians 12:13 and Ephesians 1:13-14) not every believer speaks in tongues (1 Corinthians 12:29-31). This article Is speaking in tongues evidence for having the Holy Spirit concludes:
Tongues was a miraculous gift that had a specific purpose for a specific time. It was not, and never has been, the only evidence of receiving the Holy Spirit.
Exploring the subject of speaking in tongues further, this article about glossolalia delves more deeply and has this to say:
There are some Christians, especially within the Pentecostal movement, who believe there is a supernatural explanation for glossolalia similar to that described in the New Testament. They believe that the chief purpose of the gift of speaking in tongues is to manifest the Holy Spirit being poured out upon them just as on the day of Pentecost (Acts 2), which was prophesied by Joel (Acts 2:17).
The article concludes:
Simply put, the practice of glossolalia is not the biblical gift of tongues. Paul made it clear that the chief purpose of the gift of speaking in tongues was to be a sign for those who did not believe and to spread the good news, the gospel of Christ (1 Corinthians 14:19, 22).
From a Protestant source, further reading on the history of the Holiness Movement and Pentecostalism What is the Pentecostal Church and what do Pentecostals believe may be helpful.
Conclusion: The Protestant denominations I am familiar with stress the necessity of experiencing the new, spiritual re-birth and the indwelling of the Holy Spirit. This is what transforms the believer and produces in them the fruit of the Spirit, which is the evidence of being “born again.” This process of sanctification and growing in grace is a life-long experience. Speaking for myself, I would say that reading and absorbing God’s Word, prayer, worship and being open to the prompting of the Holy Spirit to do God’s will is how we experience God in every-day life. It is evidence of having the Spirit of God, the Spirit of Christ and the Holy Spirit within. All three are inextricably linked.
However, speaking unintelligible words, or falling down and writhing around on the floor are perceived as demonic and such things have no place in any Protestant church I have attended.